I THE UNIVERSITY LIBRARY ('^ iL i^ ' H THE PENNSYLVANIA STATE UNIVERSITY "s^ ^i I / , j STATE COLLEGE, PENNSYLVANIA ^g; ^igg^^^(gg; ; !^^gjgjggijjggg {; ^.Sg%%^^9 i»^i!»t^'i ^^ THE EASTERN OBLIOUE ARC OF THE UiNlTED STATES OSCULATING SPHEROID TREAvSURY DEPARTMENT U. S. COAST AND GEODETIC SUR\^EY Sl'PRRINTKNDKN'T GEODESY THE EASTERN OBLIOUE ARC OF THE UNITED STATES OSCULATING SPHEROID By CH^S. J^. SCHOXX, ^■'i.ssistant. Coast and Gfeodetio Survey Special Publication No. 7 WASHINGTON GOVERNMENT PRINTING OFFICE 1902 Treasury Department, Document No. 2232. Coast and Geodetic Survey. Treasury Department, Office of the Secretary, Washington, J tdy i6, rgoi. Sir: It affords nie pleasure to approve the publication of the discussion of the Eastern Oblique Arc of the United States, herewith presented to the public. It appears that the value of this arc to geodesy is very great, but that the results are only incidental to the immediate purposes for which the triangulation was made. The results, however, could not have been obtained if the general plan of the Coast Survey had been less systematic or comprehensive. Thus, in applied science, as well as in many other things, the far-sighted wisdom of our earlier statesmen, who gave direc- tion to our beloved country's policies, has borne fruit. Respectfully, L. J. G.\GE, Secretary. Mr. O. H. TiTTMANN, Superintendent Coast and Geodetic Siirvcy , Wasliington , D. C. LETTER OF SUBMITTAL. Treasury Department, Office of the Coast and Geodetic Survey, Washinf^ton , D. CJidy i6, /901. Sir: I have the honor to submit to you for pubhcation the manuscript of Special Pubhcation No. 7, giving the results of the completed measurements of the Eastern Oblique Arc of the United States. This is the second of the publications intended to give the results of the principal arc measurements made by this vService, and like the first, which relates to the Trans- continental Arc of the Thirtj^-ninth Parallel, it was prepared by Assistant Charles A. Schott, whose knowledge, mature experience, and ability fitted him especially for the task. The Eastern Oblique Arc, though treated separately, intersects the Transcontinental Arc, and the two triangulations have several lines in connnon. The former extends from the Bay of Fundy to the Gulf of Mexico, and parallels the Appalachian mountain system, while the latter crosses the axes of the great mountain systems of this country, and extends from the Atlantic to the Pacific Ocean. Invaluable as the Transcontinental Arc is as a contribution to geodesy and the geography of our country, it does not in itself contain the data for determining the figure of the earth. The Oblique Arc, however, contains within itself all that is neces.sary for determining the dimensions of a spheroid which corresponds most nearly with the existing geoid within the area covered by triangulation. It is unique in that it is the first one which utilizes on a grand .scale a measurement oblique to the meridian. The peculiar power of an oblique arc for determining the compre.ssion of the earth was pointed out by Tobias Mayer (i 723-1 762), but the first practical application of such an arc to geodes}' was made by Bessel. This was before the introduction of telegraphic longitudes had made it possible to utilize .such an arc to its fullest extent. • The resvilts of previous di.scussions of parts of this arc led to the abandonment by this Survey, in 1880, of Bessel's spheroid of reference and the adoption of Clarke's (of 1866), and the final di.scussion of the complete arc here presented .su.stains the grounds on which the change from one spheroid to the other was made. Taken in connection with the Tran.scontinental Arc of the Thirty-ninth Parallel, this discussion has enabled the Survey to decide upon the retention of the Clarke's spheroid and to adopt geographic coordinates for the whole extent of this country based on a uniform system. Fiirther information as to these standard coordinates for geographic purposes, which differ slightly from tho.se here published in connection with the Eastern Oblique Arc treated independently of other triangulations, will be published in due time. Very respectfully, O. H. TiTTMANN, Supcrintoidcnt. The Secretary of the Treasury. 7 CONTENTS. Page. Introduction 19 PART I. THE BASE LINEvS AND BASE NETS. A. General rem.\rks 25 B. The b.\se lines of the e.a.stern oblique arc, their measurement, resultino LENGTH, probable ERROR, AND ADJU.STMENT OF BASE NETS 27 1. Epping base line and base net. l,ocation, measurement, and length 27 Adju.stment of the base net 2' confined in practice to the measure of meridional arcs from which to deduce the earth's magnitude. Compared with an arc of the parallel, an arc inclined to the meridian is less fa\-orably conditioned for discussing the figure of the earth on account of the greater effect of any uncertainty' in the measure of *A Lambert equivalent zenithal projection extended over a planisphere, fSee Map .\ (in pocket). 19 20 THE EASTERN OBLIQUE ARC. azimuths, and greater accuracy is demanded in the latter case than is required when the arcs follow a meridian or parallel. Oblique arcs should no longer be regarded with any special disfavor, and while they entail very much more labor, comparatively, when they are utilized in determin- ing the figure of the earth, they are well adapted, when of sufficient extent, for the determination of an osculating spheroid for the region covered b>' them. The existence of the arc discussed in this publication is the result of the necessity for a main triangula- tion binding together the detached surveys of the harbors on the Atlantic coast and forming a base upon which all subordinate triangulation along the coast could be brought into accord. The immediate object of the main triangulation was thus to secure uniformity and systematic treatment for both the astronomic and geodetic measures in the preparation of the geographic position of the trigonometric stations. This was a leading idea from the beginning of the Survey under its first Superintendent, and when fully developed resulted in the work under discussion. There could he no doubt of the necessity of firmly binding together in this way the small tertiary triangulation and traverse measures along the coast which wind, unbroken, following the indentations of the coast, from the Canadian boundar}' to Cape Florida and thence into the Gulf of Mexico, following the coast to the Mexican boundar}'. The measurement of the oblique arc was thus identical with the progress of the ordinary operations of the Survey in this portion of the country. The first period, covering the years 1833 to 1844, witnessed the executicjn of the work from central Long Island, New York, to the head-waters of Chesapeake Bay, uniting on the way the surveys at New York, New York, and Philadelphia, Pennsyl- vania, and this work was nearly all completed under Superintendent Hassler. During the second period Superintendent Bache, pursuing the same general plan, had the work carried from Rhode Island to the Canadian boundary, at Calais, Maine, on the St. Croix River, and this work was completed in 1859. In 1865 the branch primary triangulation across the State of Connecticut, connect- ing the main scheme with some older work in this region, was completed. This period closed in 1871, when the Potomac River was reached and crossed. In the third period, covering the years 1873-1877, the work was extended to the Atlanta base, in Georgia. The fourth period begins in 1885 and extends to 1898, and during this time the work was extended to Mobile, Alabama. The triangulation between Mobile and New Orleans, Louisiana, was done between 1846 and 1874. While the field work, as completed, apparently covers a very long period, the first measures dating back to the year 1833 and the last measures being made in 1898, as has been stated, this interval contained many years when no work was done upon this arc. The slow rate of progress was thus onlj' apparent, as it depended upon and was subor- dinate to the ordinary requirements of the Survey on this part of the coast, and of the general operations of which it was only an incidental feature. Part I deals mainly with the base lines and Part II with the intervening triangu- lation. The astronomic determinations of latitude, longitude, and azimuths are numerous ULl INTRODUCTION. 2 1 and well distributed over the whole arc. There are a\ailable, for the computation and comparison of geodetic and astronomic positions, results at 71 latitude stations, at 17 longitude, and at 55 azinuith stations. The latitudes depend almost exclusively on observations with zenith telescopes, and the longitudes on telegraphic transmission of time. The azimuths depend upon a variety of methods, using the pole star most frequently. Abstracts of the individual and final results of the astronomic measures are presented in Part III of this publication. The distribution of the astronomic stations over the region covered by the arc is shown on Map B (in pocket), and the two maps A and B have the .same scale as the similar maps accompanying U. S. Coast and Geodetic Survey Special Publication No. 4, containing the discu.ssion of the trans- continental arc of the parallel in latitude 39° N. Part IV contains the comjiarison of the geodetic and astronomic measures and the determination of an osculating spheroid for the region covered by the arc. Preliminar}- publication of the greater portion of this arc has already been made in the following reports of the vSurvey: Report for 1865, Appendix No. 21, pp. 187-203, ' ' Results of the primar\- triangulation of the coast of New England from the north- ea.stern boundary to the vicinity of New York;" Report for 1866, Appendix No. 8, pp. 49-54, "Report on the geodetic connection of the primary base lines in New York and Marjdand, their degree of accordance and accuracy of the primary triangulation intervening, with the resulting angles and distances as finally adjusted," and Report for 1878, Appendix No. 8, pp. 92-120, "On the adju.stment of the primary triangulation between the Kent Island and the Atlanta ba.se lines. ' ' These reports contain also more or less complete accounts of the six ba.se lines located in the arc. Other references will be given in their proper place. The present publication i.s complete in itself, and while no important facts or statements are om'itted, much .simpli- fication has been effected by referring to the publication above mentioned, covering the transcontinental arc of the parallel, the same general treatment and method of reduction of the triangulation having been emplo>'ed in reducing that arc as is u.sed in the following discussion of the oblique arc. J P A U T I . Till-: BASl' LlXl'.S AM) BASl: Xl-TS. i Till-; I'.ASi-; \.\\\'s WD l;\^l; \n\ A. (•.1'',.\i:r.\i, ri-.marks. Tlu- tinil of length i> tlu- Mime ;i> tlial u.^cii Iroin tlic l)c;(iniiiii^ oi tlie Survey until iH.Scj, \i/., an iron l)ar, i lut-tcr luni;, standardized at Paris in ijvy and (jrou^jht to this coinilry by Mr. I''. K. Ilassler in 1S05. Its use was discontimied after the receipt ut tlie new i)n)t()type ])lalinnni meters in November, issi^. This meter, known on the Survey a.s the Committee Meter, is an end measure and is rejjreseuted by an iron iKirwith .s^juare end snrfaies, now r.li^lilh (Ufaced by corrosion and jierliaps liy u.se. It will suffice to refer the reader to the fnll account .t^iven of this meter ni Part I of the ' Tran.sconti- neMilal 'rrianL^nlaiioii and the .\merican Arc of the Parallel " across the I'nited State> in the- \icinil\ of lalitnde 31/, i)iii)lished by the Coast and C.eodetic Survey in i. In that pnbliialiou, after some liistorical notes, the results of the lunnerous comparisons, direct am! indirect, 1)\ different ol)ser\-ers, liy diderent methods and at different times. are coniiiklel\ set forth, and the hnal conclusion is reached that this bar at u" C. repre- sents so neaiTv the lenL;th of the i)rotot>i)e meter that no relial)le value of the difference can be- slate-d. TMie weii^iited mean of all e-omparisons ,uave the result i ^o-2Hzi:o6n, and in all eiinipr.lalions dependin.n upon this .standard it has Injeu taken as etjual iti len.i;tli to the proiotspe- meter with a probable error of about three-cjuarters of a micmn. There- are six base lines irrefjularly distributed aloni; the arc. and they are descril>ear.UUs useel for the measure, nan'ie of observer, com])Utation e)f len.i;lh and hnal result, with its proKible erre>r. .V sketch of each base net is jiresented, and it is followeel by the abstracts of hi>ri/on- lal dire-e'tions, obse-rxcd and adjusted, for e.ich station forming; i>art of the net. These absiiaets e-onlain the- following; inform, ition: Count\- anil State, elate of measure, inslru- nie-iU Used and olisei\e-r's n.inie, ,ind also, in the first e-olinnn, the lUunlKT of each ilirec- tion. Tlle-^e nmnlu-is, when in iKUenthescs. in licite the correspomliui; eX)rrections as ,i;i\en b\ llie- net ,hljn>lnunt . In the ,L;re-al majoriiv oi ca.ses liinr/ion thetHlolites were eiiijilov ed. and foi ilie-se iRSSels method ' <.A reiluction at the station was usetl. When /■(-/>(-duction <.A relative weights. HeK>w the aKstracts of ilirtvtions resultiiiL; fioiii st.uion .uljiislment there is i;iven the probable err«>r of a simple obscn'a- * Sio W W . \\ riijlil's " 'rri'iUisc on tlu' .\iljii-.lnunt of Olwcn-atioils." New V,■ t Uiiil., p 1 >) .nul foil . al>a )> Ji: .itul toil. 26 THE EASTERN OBLIQUE ARC. o'455 5'J' tion of a direction (mean of the direct and reversed series) deduced from (?,'= — ,-.-— , where ;/ = number of observations, ^ = number of series, d = number of directions, and J= diiferences of observed and adjusted vahies. The figure adjustment of the triangulation generally proceeds on the supposition of equal weights to all directions used in the adjustment, except, as in the case of the Epping base net adjustment, where special weights are introduced.* To carry weight equations from the station adjustment into the figure adjustment is not practiced or favored in the Survey on account of the increased complexity and the doubtful advantage of the pro- ceeding. The errors brought to light by geometrical conditions, and which have been called triangle-combination errors, are of a different character from those developed by a comparison of the measures made at a station, where defects of centering at observing and observed stations, effects of large local deflections of the vertical at a sta- tion, persistent lateral refraction along a line, etc., do not .show; that is to say, weights pertaining to one operation are not those proper for the next operation. Further par- ticulars of figure adjustment with statement of formulae may be found in "The Trans- continental Triangulation," Part I. Foi the computation of the sides of the triangles Legendre's theorem was used, and since none of the lines of the oblique arc are very long the .spherical excess was computed by the simple formula ab sin C 2/3^ p„ sin i" where C = the plane angle included by the .sides a and b and the subscripts to ft refer to the radius of curvature in the meridian and in the prime vertical. Appendix No. 9, Coast and Geodetic Survey Report for 1894, page 291, contains a table to facilitate the computation of the spherical excess, the argument being the latitude of the center of the triangle. The computation of the geodetic positions along the oblique arc is made according to the formulae and tables in the same appendix, the differences in latitude, longitude, and azimuth for two points of known distance and azimuth being given by [ ~Aqj — s cos a. B-\-s- sin' a. C-\-{,Sq)y D—h r sin' a. E I A\ — s .sin a sec q)' . A \-Aa = A\ sin >4 ( hash nkt, maink, 1H57. Locdtioii , iiintsiirriiiiii/ , and iisitllitii^ Iciii^lh of thr Jippi/K/ i>a^( linr, Mairit' . iS^y. Tlu- silL- ot lliis Itasc is on ]vp])in^ I'laiiis, near ClK-rryfield. Wa^IiiiiKton Counly, Maine. A reconnaissancx- of the- locality was made in is.s.v 'I'xl tl>^' iiieasurcinciit of the base followed in Jtd\- and August, 1S57, under the immediate direction of Sujxrriji- tendeiil A. I). Hache. Tlu- Aiiiiiia! Ri|)(.rt for 1.S65, A])ix:iidix N(j. 21, pa^es i?i9-iyi, contains a full acc(Jinil of the measure and of the result. It will therefore suffice to present here onl\' the .salient points of the o])eration. The measure was made wilii the Hache-Wurdeinann contact-level coiniHrii.sating a])paratus, and is the sixth primary line where this ajjparatus was emj)loyed. the Dau- ])hin Island base, Alabama, beini; the first, an account of which is given further on ( ij. v. ;. The apparatus is fully descril)ed with illustrations in Coast Survey Rejxjrt for i''^54. Appendix No. 35, and reprinted in Coast vSurvey Rejiort f(jr 1.S73, ApjKrndix No. i.;. The essential ])art of the ajjparatus consists of two 6-meter bars, (jne of bra.ss and one of iron, placed jjarallel to each other, one being abo\e the other and firmly coiuiected at one end. At the (opposite or free end is the lever of com{)ensation. so pro|Kjrtioned in its arms with respect to the actual and differential expansion and contraction witli changes of temi)erature thai the end of liie ap])aratus Iemain^ at a constant distance from the opposite end. The spirit-level contact piece terminates in an agate, ground to a knife edge, whereas the agate at the ()])posite presents a slightly convex surface. The appa- ratus was standardi/eil 1)\ niean> of a standard 6-meter iron bar. the length of which was determined at dilTeient times in terms of the Conunittee Meter. The length of this base is about S'yj kilometers ( or 5'4_' statute miles ■, its middle point is in latitude 44° 4o''S and in longitude 67'' 53''. with a mean a/.imuth of iij6° 54'. Much labor had to be spent prei)aring the groinid for the measure by leveling it. removing l)owlders, and overcoming other obstacles, the handling of the apjuratus deuianding a wide and fairly smooth roadwax , The average height of the tuivs aUive the mean tide level of the Atlantic was 7(>"4,s meters. The d-meter kise l*ars or tulx.-s were compared with the standard o-meter bar just before and inuiiediately after the Ui.se measure. Taking the lcii'-;th of ilie latter and ilscoefiicieiu of expansion as ileterniineil in i860 and published by Assistant J. \\. Hilgard in Coast Survev Report t\>r iSfu. ApjK-ndix No. 26, viz, .S'yijij 941 meters, and o'ooo 01 1 54 for the centis^raile scale, the following residls for the length of the tubes were obtaineti: Three sets of 23 comp;iri.s*.)ns. made with Saxton's letlecting ci)mparat(»r ■■ on July toth and 17th, gavetulK- No. i shorter than the stand, 11 d I at iS''3C.) 1 3LxV4ilivisions of the compar.\tor and tulv No. .'shorter 1 (."kSS" 7 ±-'o i: z'2 * Tin iii-ti vimvnl i> kimwn ii-. Siixtons pyrometer, ami it i> aocrilxnl in drtiiil. with ilUi.'>(rnlii>iiv in the Report of thf SuptTiiUcmlciit of WtiKlUs ami Mias>irc< lor is.i^ ami thr Kcjx>rt of the >iniic Imrcau for !■♦.• cvtmainv on {vi^r ir<, n miicral lU-scription of it. Out- larii of the screw equals ,v.'i7ii scnle ilivisioiis nml one t\;r niu-rxiti*. Tho hfjul \*i vliviiU-tl into ux> tlivisious. 28 THE EASTERN OBLIQUE ARC. divisions; again, after the base measure, on August 6th and yth, from 4 sets of 27 com- parisons, tube No. I shorter than the standard (at 2i°'oC. ) i 411 '8 divisions and from ± 3-3 4 sets of 23 comparisons tube No. 2 shorter i 195 '3 divisions. Having regard to the =h2"9 weights, the abo\'e comparisons give the vahies for length of tubes, for No. i„, 5 '999 459 o meters,* ±49 for No. 2, 5 '999 750 6 meters. ±49 Although the comparisons of the tubes with the standard bar were made with rising and falling temperatures, there remained an uncertainty respecting the indication of the thermometers in air giving the temperature of the metallic bar even within }^° . Furtiier, some allowance had to be made for any defect in the mechanical compensation, for pos- sible error in making contacts and transfers to the ground, and for other small uncertain- ties in connection with the base measure, and this was arbitrarily fixed as ± g'j /<. The probable error of the length of a tube during the measure was taken as ^ji^'g)- + (g'j)'^ = =t io'9 yu, hence that for the whole length = i 453 X io'9 yU = o"oi58"', which equals 55X650 pai't of the length. In this case, as in that of the other bases of this arc, except the Atlanta base, the single measure fails to provide proper means for a more reliable value of the probable error of the length. We have for the length of the Epping base: I 452 tubes of mean length, 8 711"' -4262 One odd tube. No. i, +5'9994 Correction for inclination of tubes, — 2'So40 Defect of last tube at East Base, -fi'425o Reduction to half-tide level of ocean, — o'i044 Resulting length of base, S 7i5"'-9422 rb o""oi58 And its logarithm, 3'9403i434 ii= o'oooooo79 The Eppiuij base net and results of its adjustment. As shown on the following sketch, this net of triangles is included within the primary quadrilateral Humpback, Mount Desert, Howard, and Cooper, and involves 6 geodetic points. The figure is a ver>' strong one and demands that 35 geometric con- ditions be satisfied. The reduction of this base net is complicated on account of the employment of both direction and repeating theodolites, five of the stations having been occupied with the latter instruments. An account of the adju.stment of this base net iscon,ained in Coast Survey Report for 1864, Appendix No. 14, and may be referred to for particulars; the results are here transcribed, except that the notation has been changed for one more convenient. In connection with the station abstracts there is added a column containing the approxi- *Comparing these values with the corresponding values of 1847 (Dauphin Island base) and of 1872-73 (Atlanta base), it will be seen that the lengths are not invariable, but it should be noted that one of the agates of tube i was acci- dentally broken in 1855, and after the new agate was substituted the tube was found to be o'43o millimeter shorter than before. Coop«^> Jhiniphnrk IIASI', I.IN'I-.S A NO I'.ASK NKTS. 29 mate value of tlic ])rol»;il)lc crnd' ol a resiillin^ 'lircctioii, deiKrii'lintc on tiic- I'ortmila o'455 ^/i ..... ... ^ -■ .. -p-^.' „, in case ot (lirccliou ohscr\'atioii'i. In <.a>>c ol r<-ix:titi'jn>i the nroli- s (ciiag. cocli ij ' ' alilc error will (le])en(l ui)on the cotnparison oi a reTiiltin;^ an^le with each of its 20 measures Teacli of 3 repetitious direct and 3 rejietitions reversed;, from which an averajre and a])])roxiniale '.alue r,t the probal»le error of a v///;'/^' measure of an ant■ sub- tractin<; the correction to the initial direction from v:\c\\ of the corrections to the other directions, as ,i;i\rn in the precedinj; colunui. i In the adjustnu'iil of the ba.se net special wci.^hts were nssij^ned to the directions, as exiilaiucd ,it U'ni;tli in Coast vSurve> Repot t for lS(>(. If we lU'duce the probable el loi of a direction from the closiuv; errors in the xum of the auL^Ksol the 40 Iriaui^les, we liud from the sum oi iIk- >t|U. ires of iJK-.-e irror-> the mean closiiis; ciroidf a tri.niL;lc ./■''"* ^' -; rt i"'oo, hence the proUible error of a direc- > 46 ' tion = 0(174 \ 1 00 y'o - zfco"'3o, On the other hand, the avera.i^e value of the jiroliable error of obser\Mtioii oi the 11(1 directions in the net is about rt o""J4, whence the triaui^le combination error *, - v(,o"3o)°— (o*24)-" — ±o""i7 tnearlx b and the square oi this was adtleil as a rcz/.s-Ar/// to each ol the prexiously deduced squares of the olwervitiii errors. W'c then have >■-' ■' • ." ind the weii^lu to ,ui\ directiini p The values i>f /> thus have *Tln- hnlf l>nioktt iiiilioatfs sum »f siiiiiliir (lUiiMlitic". ilisri-ijanlinij their sirh- tl'ho lucaii of till' .| vahu-s of ,-, .U-nvi rtiul A" 1 with ihc -s " thcvxlolilr i» - t ' v\4 nml •!»• mean of tin- s valius v>f r-i lUrivnl from a siii(;U- iiua»urc (.;/>. ami sA" ■ with the .-v"- tr{)ratiii|; (hcuiMilr i» A i"i(>, or one measure with the first instniiiieiit is alxjiit et|iial in acv-nnu-y to three with the latter. 30 THE EASTERN OBLIQUE ARC. smaller range than the}' would have had without the addition of the constant; still the maximum weight is to the minimum weight as 5 "4 to i. The effect of the intro- duction of weights is small in cases like the present, a base net of great complexity and fair measures. There was no special necessitj^ for a reduction of the horizontal measures to sea level on account of the elevation of the signals sighted. The following table gives the approximate heights of the ground at the stations: Meters. Feet Epping East Base, 77-6 255 Epping West Base . 72-9 239 Burke, 1295 425 Tuiik, 350-5 I 150 Pigeon, 95 "9 315 Humpback, 451 I 480 Mount Desert, 464-9 I 525 Howard, 82-0 269 Cooper, 224 735 The largest reduction for latitude 45° and « = 45° ( nearlj' that of the line Epping East Base to Motmt Desert) would amount to only o"-o25, a correction so small that it may be neglected. Abstracts of resulting horizontal directions observed and adjusted at stations forming the base net, 1S56-1S59. Eppinimtni( tht- hate iii't , /.V5<5-/.V5(>---continue'I. Iiurlealin>» the<*lolitc No. 43. C. (). I'.oiitL-llL-. oljservcT. No. of direi- tioiis. ((liJL-ils oliservi-il. HesultinK,|ir.c Ap,.roxi S'r'onT'r:^' '" lioiii from -.lalK,!! male \,r>,\, ,,^."",1?,,^ Illrllt pp. .'KljustmeiU .iMc crrori r3 I 1 Iuin]il):ick 14 I I•',l)])ill^^ West IJase 15 j C()<)])CT 16 I Ivp])iii>^ Ivasl Base 17 ' IluwanI 18 i I'im<)ii 19 I MduiiI Desert 20 ; Tunk 35 5'^ 55'i.> 62 41 3670 75 I" 3 '■4'^ i"5 3" I ''■^4 17^ 5^ 5i\>" 236 (K, \ys\ 3'5 37 5299 "■32 .,•36 "■33 "■33 "■33 "■34 '"•34 "34 (rr«») Itt'lft) "S^V 5^' 159 '•'7^ 37 -Vv ofntif 32<>Sy o.Syi 15749 ■•■397 5" 9'J3 "442 ^^^'^^ "■326 533 1^ ridliaUlc ti ror (if a siiiijlc oIiscia aliuii ( 3/). and 3 A', int'a ilireition, /•, — • it" .i^i. Nninl)cr of an>;le-. adjusti-il, i.|. 'I'loik, llaindi'k Connly, .Maine. ()cl()l)er 27 lo ()cl<)l)er 31, iSSy. 25 "' re|K-aliiix iheiwlnliu- No. \\. C. ( >. Boulelle. oliserver. ()»> (X'Olt 67 44 5^53 •\> 49 3"'54 I iS 30 i>.*S"3.s 144 27 2916 201 !l 04-45 275 5*-" 53"'^ Probable error of a sinijle observation I 3/^. ami 3 A'. 1 of a ilireclioii, f-, = :»r I "'37. NuinlK.-r of ail>;le> adjusted, 1 -• /'/;,'(■('«, Wasliinnloii i.ounl\ , Maine. t)clober ly to 25. I "-"Sy. 25 '" rciH-atinj; llic<>lile Ni'. 4^ C. (). liouteile, observer. 21 I Inni])liaik 22 ''•PP'"K \\'est Hasi 23 ICp])in>i Ivist Ba.se 24 Hurke 25 Pij^eon 26 IMonill Desert Sannders :o-4S O'tJIHI (MJ'IJI I 1 U-4.S 0S36 55 '^94 o'46 o'i>7i 1 3 i)-46 "■'>75 "7-5"5 046 01 54 293' 4 "•47 yV22\ l»4'226 "5' 27 Monnl Desert • Sannders 2S Tnnk 29 Umke 3" llnnijiliaek 31 I'lppiii!.; West Ikise 32 Isppini.; I'!,isl It.i.se 33 I loward O IX) (K>IX) 45 00 4299 74 49 "2S6 90 12 3.S14 92 09 19-50 104 56 40-61 '23 57 37' '7 1 7h 41 3 1 -69 Prob.diK- erior of .1 single obstixiiion \ 3/ '. ,ind 3 A". I of .1 direction, f", = 2: l".ll. NuinltiT of ;ni)»U-> .idjusti'd, \.\. -0-27 O'OCM OO'IKXI I)' 29 0-27 -0326 "2-5.U '^^■25 ■^^477 3N-6I7 026 0-033 19467 0-26 1-4S2 42 .*)2 0-27 • 0-303 37 473 ''■25 • "5.^6 -,2 22*1 32 THE EAvSTERN OBLIQUE ARC. .^/>s/rinis of irsii/liiii; horizontal directions olncrvcd and adjusted at stations forniinff t/ie hase net, /S^6-/S^g — continueil. Huiupl)aetc, Hancock County, Maine. July 19 to vSepteni?)er 6, 1S5S. 75'"' direction theodolite No. i. A. D. Baclie and G. \V. Dean, observers. Xu. of direc- tions. Obje 34 Cooper Azimuth Mark 35 Howard 36 Epping East Base 37 Epping West Base 3S Pigeon 39 Burke 40 Tunk 41 Mount Desert Ragged Mountain Saunders Mount Harris Resulting direc- tions from station adjustment. Approxi- mate prob- able errors. Corrections from base net adjust- ment. Final seconds in trian- gulation. / '/ " // r/ 00 00 -000 d=0-I50 OQ-QOO 39 37 40-23 0-163 40-403 39 45 46.385 0-126 +0-605 46-990 59 43 io'4oi 0-136 +0-1.^,5 10-536 69 3S 48-051 0-151 -^- 0-084 48 -1 35 84 09 57 '099 0-125 —0-223 56-876 85 14 25-280 0-142 — o-o86 25-195 102 22 1 1 -498 0-143 +0-093 11-591 114 33 50-877 o'ogo +0-779 51-656 154 2S 20-545 0-132 165 12 47-118 0-131 I. So 36 29-988 0-169 Number ( >f positi( ins of circle, -V. Probable error of a single observation of a direction , <', = ■91. JMount Desert, Hancock County, ^Nlaine. August 14 to October 14, 1S56. 75' No. I. A. D. Bache and G. \V. Dean, observers. o / // // Isle an Haut Mount Harris Saunders Azimuth Mark 42 Humpback 43 Tunk direction theodolite 44 I Burke 45 46 47 Cooper Epping P 8 59 24-726 fi7i 09 49736 0-148 - 0-399 49"iS5 '- 26 49 49'584 ii75 20 34-430 0-115 +0-068 34-346 '31 00 34-278 1176 36 26-634 0-132 —0-062 26-420 ^2 16 26-482 ./199 47 46-624 0-132 +0-756 47-228 '55 ■^7 46-472 (201 ■ 57 46 49-121 O'lIO +0-390 49'358 26 48-969 Probable error of a single observati on of a direction, e^, = ±o"-86. liASK LINKS ANIJ UASl-, Nl'.TS. n Alislnjrt\ (if rr^iiltiiii; lioii-UDildl t/inilioNs iih.un'iit itiitl itdjustid at sliiti(iii\ ft)\ \V'asliin),;l<)n Couiilx , Maine. Auj^usl 30 lo Septenit)er 16, 1*^59. 75 '" ilirection the'xloliti- No. I. .\. 1). Hailu- .1111! ('.. W. Dean, observers. ilirin " •• '■ / // " " // ft (X) H,l*t, ■ 01.10 <r 1 '9 25 944 "■'77 '1 1 12 iS^\2 22 <'2 \\\iU 21 •, o-.^S ^•'5"' .5.^ ,v> 40- 141 191 0204 1" V45 5' •Vl 41-50.5 "-'73 • 1 231 ;2 7^'i |(..S 01 .'7 996 oil 1 o'o22 2^'o: '' '23 5' 19 227 '1 MM 19 21/. :73 43 51-973 IC^I 1S9 2S 45-^43 0161 Cliaincook I'rinee Regents Ri'ilonbt C.rand Manan Tii'seott l\ot'k (K) 00000 .VS 36 49-O.S2 54 40 14-493 6S 43 51-6.S7 I loS 5^5 1K)3,S5 I (1 00 (H)'l»«) I '57 47 '"'-7'^; \ 4S 50 5" 'I'M 160 II .10754 1 5 1 15 ;, I ■369 I 192 12 4301.1 I S3 16 33 -^21) 294 13 (vS-,S,)4 I1S5 \c 39-.IU) Nninlierof posilionsof eircie, \'. I'robaliU- errorof a simple observationof ailireclimi. c, =:t l"li). Ilowar.i Mounl Desert lUnke Ilunipltaek .\/iiniitli .Mark 01 17 197 23S 161 " 133 iroiitt 1 1 >'i ■ ■ • OIS.S 0-641 52 •■45 "149 "57'^ 3 1 94"^ I" '5^7 33 "42 .59-57: I'li'iMNT. H.VSI-; Niri' .vi>ji s'i"mi-:nt. ( Vi.s(7-riis. 1 0= t 217S07 I 0-40133^5) o37S95(^4) , o•hU194^32^ 1 •53''^5i^( 3 ' i • >'-Si3o2i 3; -2(>i(x.7(37) i 1-20305(36) 002237(7) (0-92756(30) II 0= 10-283 I (S)- (12) , (37) (36) • (5) (4) III 0= 0-698 t-(32) l3'-'Vf(3>^^ (36) : (5) (7) IV 0= o-8ti7f(3i) t3o)+-(38) I37)l-(ja) (9^ V 0= 6.125S8 ; o-8tx)64(3i) 5-3l^)l>S^ 24) • 10-47161(39) ii-2:6«.\ji 38) 6-J»xi62t3o^ ' ^''754431,37^ 0-167821 12) o;o2i2i 10) • o-46<.k>.|i o) 4U)J Xo. 7 — 02 .^ 34 THE EASTERN OHI.IOUE ARC, VI ! o= VII o= VIII o= IX o = X o^ XI o= XII o= XIII o= XIV o= XV o= XVI o= XVII o= XVIII o^ XIX o= XX = XXI o= XXII 0= XXIII 0= XXIV 0= XXV 0= XXVI 0= XXVII 0= XXVIII 0= XXIX 0= XXX 0= XXXI 0= XXXII 0= XXXIII 0= XXXIV 0= XXXV 0= [The log- Ohsei'z'afion I'qiialioiis — continueil. : + r292-^(io)-(9) + (3i)-(29) + (iS)-(t4) :-|-o-768-r( [S)-( i3)^(39)-(3S) + (3o) -(29) = +o-o84S3-ro-257oo(i6)-o-54S4i(i4) rO-29i4i( i3)+o75443(39)-i'9574S{37) -1-1-20305(36) 0-40132(5 ) -; o-i6676( 2) -0-56808(4) -o-7S8-j-(i6)- (i3)^-(39) -(36)+(5) -(2) -I -34263-0- 182841 II) -o'65278( 10) -1-0-46994(9) +0-80064(3 1 ) — I '56540(29) i o-76476( 28 ) -r-o-43254( 25 ) - -o-6o454( 24) -|-o- i720o( 22 ) -2-555-: (20)- (18) -K (29) -(28) I- (25) -(24) -r726+(25)-(22) + ([i)~(9)-f(3i)-(28) :— 0-6877 1-^0-3 151 2 (32) --1-07988(29) -1-0-76476(28) -(-0-43254(25)— 0-73688(24) -0-30434(23) -1-0-43596(3)— 0-65063(2) +-0-21467(7) -o-929^-(i6)-(2o)^(24)-(23) + (3) -(2) - 1 '58338- 0-73062(23 ) -0-81676(22 ) +0-08614(21 )-|-o-32768( 40) -I -53073(37) + 1 ■20305( 36) -ho-4oi32( 5 ) — o-836o6( 4) 4-0-434741 3 ) + 0-I53-(40)-(37)^(l2)-(ll)+(22)-(2l) +0-22432 ^o-65422( 44 ) - 1 -98508(43 ) -f T -33086(42) ^o-97432,( 41 ) - 1 -65748( 40) -1-0-683 16( 39 ) - o-2i525( 13 ) -o-25436( 20) -f 0-0391 1(19) -o-907 + (i3) --(i9) + (44)-(42) + (4i)-(39) -i-ii7-(4i)-(4o) + (2i)-(26) + (43)-(42) - 1 -832i8 + 2-20947(46)-2-62575(44)-Lo-4i62S(42)^o-374S4(4i 1-0-81586(39) -)-o-44io2(36)-fo-03977(5)-o-9ri52(2)J-o-87i75(i) -i-27i + (2)-(i) + (46)-(44)-^(i9)-(i6) = -0-44146^0-67443 (30) -0-73 156(28) +0-057 13(27) +0-18656(48) -I -51742(43) -hi'33o86(42) + o-97432(4i) -1-61457(40) +0-64025(38) -i'35S + (3o)-(27) + (48)-(42) + (4i)-(38) +0-92970 fo-44io2( 39) -I -02088(36) -1-0-57986(35) +0.66575 (53) -I -70358(52) + I'o3783(5i)+o-3599o(i7)-o-4i562(i6)+o.o5572(i3) = + o-303^(2)-(6)+(52)-(5i) + (i7)~(i6) -o-i34+(36)-(35) + (53)-(52) + (6)-(5) -I -36912^-0-66575(53)- 1 ■ooo27( 52) +o-33452( 50) +o-49i53(47)-o-82493( 46) +o-3334o( 42 ) +0- 14829( 4 1 ) -0-72815(36 ) +0-579861 35 ) = -r7i6+(i)-(6)^(52)-(5o)H-(47)-(46) = +o'5 1527 fo'3589o(4i) -0-57388(38) -0-214981 35 )+o- 17014(53 )+S-94070( 49) —9-1 io84( 50 ) +5-94358(48 ) -6-07800(47 ) -ho- 13442( 42 ) = -o-o56+(33)-(27) + (48)-(47) + (5o)-(49) = -i'75954+o.33673(58)-5-337i9(57)+5-ooo46(56) +2-88157(45) -3-29785(44 +o-4i628(42)+o-37484(4i) -0-39237(39 )-!-o-oi753(34) = + 1-216 f(i9)-(i5) + (57)-(56) + (45)-(44) = +o'38o+(4i)-(34) + (58)-(56) + (45)-(42) = +o-822i7+4-83i53(57) -5-00046(56) -^o-i6893(55)+o-oi479(54)-o-57i45{5i +o-55666(5o)+o-38566(47) +2-49591(44) -2-88157(45) = -r463 + (47)"-(45) + (56)-(55)-|-(54)-(5o) differences for i'' are given in units of the fifth place of decimals.] I'.ASJ-. IJXI-.S AM) l;ASI'. Nl-.TS. Tile ic ari. a> tollow-. nil , 1 /. iiii ' /' iiii ' . 1 /■ I 0.094 43 ..012 5 ^ 4 .35 00 16 45 0-041 51 (> W 1 Id i6 "■'.V; 26 "■2.V' :i'> ""19 V' .. ■,.,■•, S6 7 D'l 12 '7 o-ip -7 " ' ' "5 37 "■"53 17 ....JS 57 s ((■()6,s I.S ,.-||.S 2.S o-lol :>^ .,-o|'> 4^ M-.,,J 5^^ 9 oviyo '9 "I'll 29 "■"91 39 "■".5" 19 "■"5' ' III "''>9.i 211 .ii,K, ^" II (KjS -1" DOS 1 5" 0-2 TliL- corrclaU- and iiomial eijuatioii.s iiia>' l)f t<>mul in Coast Stir\-L-> kL-]» i:.\s 1 131 (1-1 17 (231 "■351 1331 "■26;, 1 14) • 0-412 ( 2-1 1 "594 134) : "■<)56 ( '5' 1 1 i(S 1 1 25 "■435 ' 35 1 ir;,6y ti6i "■49-' I 26 1 "■".57 136.1 11-66.S ( 171 1 -(Kl.S '-'7 "357 '37' (1-22(1 ( iSi "■514 ( 2.S 1 "■6S3 1 3.S 1 "•731 ( 19 • "■559 (291 o- 1 21 P 1 39 ' (1-6.1' ( 20 ) (1'2(19 (3"i "39" (.}ni l-'or i-lu-ck 1 wi- lia\i- :;•(/..-:■ 1 ■ • 1 7 1 3 1 :itiil |.v C • 1 7'14- I • 1 25 1411 "■"54 142- 0-179 '4>i 0-196 (44 "•4"9 145' 0.061 ( 46 i 0112 I 47 0.419 i.\S. 0-2S2 I 49 ' i>- In; I 5. "'43 '52 ..063 (5;, "5 12 I 54 ■613 247 'iMu- jiriiiialiU- error ol .1 diri.-i-lion of iiiiil. U(.-ii;lu is tlicrcfon.- "■"74 ./'-'' ('■(i; 1 ./ ' ■■* -I I ". p). 'Plu- ri-tMpr(>(.'al of tlu- a\L-ia.!4(.- wt-ii^lil of a direction, or 1 /- fi|naU .iimi, hciict- tlic prolialiK- (.rror of an ol>s(.-r\-t-d dii\-clion (.-([nals 1 41) .' r ■ .j" and that of .1:1 aiii^li- I- i>".('7. r.iuk(- l-!]ipiii.i; West lia.si- I'^ipiiiv^ I'!. 1st Base ■riMils l-^ppilii; Wr.st Ua.-ic I'!p]>iii,v; Ivisl li.i.-.!.- Ol>-.il\> C.illn lioM ical atiijU- Sphi-r "u-al 11 -(VS.. 35 93" ' 11 \>~<.) 0-422 1 1 32S .1 -ivSi ■ -ivS»i I2-9S.. " 'IV-) 1 1 -gi l^ 3.J -9 \h o -vVvS n ■ I 22 3ti -g^sS n -1167 I 31 I iS -329 o •06S * With chim.nvd imtutidii. llu- i>rcsciit one lii-ini; 111. nc c\>tiveniciit for i>rinliiii; ;i~ I U is not iiuitt- cx.u-t, I'oi- llu- ri-asoii lliat :iflfi llu- ni-iu-r.il liutirc ;>iljii-tmrnt h the I'oii-fclions to tile ilim-lions wt-ii- not :issni-i-«l .in>l h:ul to In- fiirtlu • lidol' tlinl rciiort coiit-l.ilf xwi for -vhm; n-ail .;.|.».l; I I'lililishid in I'oasi Shim \ Ki i>oil fot iV<.,. ji). I.01! .lis lam-cs 3 -iM-i 314 34 4 i3'^' 343 '■'4 .| ■032 670 7s 3 i>4o 314 34 4 322 77^ '^• 4 I3-3JS S 715 «^»4 2 13 751 .Vi^ r 36 THE EASTERN OBLIQUE ARC. No. 13 14 Re^ulinii^ angles and S7(/(-.V <)/"// w Epping basi' net , jMainc — continuea. stations. Ob serve / d angles. Correc- tion. Spher- ical angles. Spher- ical e.xcess. l,og. di.s- tances. Di.stances m meters. Tunk 50 45 II -850 -0 -039 II -811 -094 4 -032 670 78 10 781 -291 Epping West Base 49 01 45 -330 +0-300 45 -630 0-094 4-021 662 33 10511 -443 Burke 80 13 02 -640 + -203 02 -843 -095 4-137 32.S 24 13 719 -'83 Tunk 34 40 37 '840 -0 -945 36 -895 -106 4-13S343 64 13 751 -296 Epping East Base 25 46 43 '060 + 1 -591 44 -651 -106 4 -021 662 33 10 511 -443 Burke ]i9 32 38 -490 +0 -283 3S -773 -107 4-322 77S 80 21 027 -072 Pigeon 19 00 56 '560 — I -180 55 -sSo 0-17S 3 -940 314 34 8 715-942 Epping West Ba,se 64 55 oS '300 + 0-951 09-251 0-178 4 -384 324 57 24 228 -391 Epping East Base 96 03 55 '500 + -402 55 -902 0-177 4 -424 896 92 26 600 -936 Pigeon 33 44 59 '030 -0-174 58 -856 0-197 4-138343 64 13 751 -296 Burke lOI 48 19 -820 - I -005 18-815 0-197 4 -384 324 56 24 228 -390 Epping East Base 44 26 42 -600 +0-322 42 -922 0-198 4 -238 S47 61 17 331 -957 Pigeon 49 oS 34-310 + -629 34 -939 -405 4 -322 778 80 21 027 -072 Tunk 60 37 58 -620 + "084 58 -704 0-405 4 -384 324 57 24 228 -391 Epping East Base 70 13 25 -660 + 1-913 27 -573 -406 4-417 660 18 26 161 -352 Pigeon 14 44 02 -470 + 1 -006 03 -476 -099 4 -032 670 78 10 7S1 -291 Burke 141 07 55 '670 -0 -925 54 -745 -100 4 -424 896 91 26 600 -936 Epping West Ba.se 24 oS 03. 450 -I -373 02 -077 -099 4 -238 847 61 '7 331 -957 Pigeon 30 07 37 750 + 1 -809 39 '559 0-295 4-137 328 24 13 719-JS3 Tunk 76 42 32 -630 + -990 33 -620 0-296 4 -424 896 91 26 600 -936 Epping We.st Base 73 09 48 780 -I -073 47 -707 -295 4 -417 660 18 26 161 -352 Pigeon 15 23 35 '280 + 0-803 36 -083 0- lOI 4-021 662 33 10 511 -443 Tunk 25 57 20 780 + 1 -029 21 -809 0-102 4 -23S 847 61 17 331 -957 Burke 138 39 01 '690 + -723 02 -413 -102 4 -417 660 18 26 161 -352 Humpback 9 55 37 '650 — 0-051 37-599 0-105 3-94031434 8 715 -942 P^jping East Base 27 41 01 TJIO + -320 01 -330 -106 4 -370 860 02 23 48S -756 Popping West Base 142 23 2 J -940 -0 -551 21 -389 -106 4 -489 329 42 .30 S55 -275 Humpback 25 31 14 -879 — -220 14 -659 0-352 4-138 343 64 13 751 -296 Epping East Ba.se 79 x8 13 -910 — -400 14-310 -352 4 -496 419 39 31 363 -129 Burke 75 10 31-480 + -609 32 -089 o'353 4 -489 329 43 30 855 -276 Humpback 42 39 01 -097 -0 -042 01 -055 0-441 4 -322 77S 80 21 027 -072 Epping East Base 53 31 30 -850 — I -192 29 -658 0-441 4-397 174 17 24 955 -954 Tunk S3 49 3" '540 -} -070 30 -610 0-441 4 -489 329 43 30 S55 -276 Humpback 24 26 46 -698 — -358 46 -340 0-525 4 -384 324 57 24 228 -391 P^pi-iing East Base 123 44 56-510 + 0-721 57-23' 0-525 4 -687 346 90 48 679 -590 Pigeon 31 48 17 '670 +0 '335 18 -005 -526 4 -489 329 42 30 S55 -275 1,1 iS 19 15. ksi-: IJXlvS AND 1 5ASK NKTS. 37 k;-., llini^ (lllL'Ji^ iii(t k/i-s III till- /■.f>f>IIIL, fnisi- Hi- /, Maine — coiiliiiueil. Slrilioiis. 01. iirvi-( / 1 .iIIKlrs // Correi lion. ical aiiKlt--.. S|»htr- ical rxec-,.. !.'-« .11-. laiicr.. I Iiiiii]jli.i(k '5 35 37 229 ..•i6<^ 37-'529 5^' •59 167 4 -370.S600-, 23 4HS 7S7 1 1 iiiii{ili.u'k 32 43 23 -447 '(XK) 23 45^ '.■26.S 4 137 V8 24 '3 7'9 02 IvjiliiuK \Vrsl I! 'ISC 7<> 31 40 -yK*. • " ■^>74 4' '^^St '. ■26.S 4 •397 '74 '7 21 9SS 9S» •I'liiik ^>7 11 5^' ■530 (.■S;/) 55 694 o-26.S I -370 .S6.J03 23 4^*^ 757 1 1 min)l>;u'k ' 1 3' rKj •() |.S " 'y>^ ().S74<. <.-242 4 424 896 91 26 6r«. 956 r'lipin.H West 15 ase '5-' 41 29 •760 "■399 29-361 0-242 4 '^1 34^9' 4S 679 5 396 "■•95 4 021 662 33 10 511 443 liiirkf 44 22 07 'OIO ()-326 (16 -6X4 "■'95 4 ■',97 174 IS 24955 "954 'I'unk iiS 3'> oS -^So '••■S75 07 '5"5 "■'95 I 496 419 40 3' 3'>i '3" I Iuin]il>,u-k I 04 2S|,S( ' "^''Lv^ 28-319 I) -024 4 -23.S.S47 '" ' 7 33 1 957 PiK'roii 1 5''' 41 ^^o "■5"9 40 -.S5. •024 4 •496 (19 39 3' 363 124 liuiki.- 176 5'^ 5' W"' -"■397 5"9f'3 0-025 4 -6S7 346 9 1 4S 679 ■5V 1 Iiun])li;iok IS 12 14 399 ■ ' ' '3 ' ^' i4 7'5 -321 4 417 660 IS 26 161 352 riKccMi '7 20 16 ■640 • " 293 ■''■933 320 4 ■397 '74 '8 24 955 ■954 'I'liiik 144 27 29 ■|6() ! fi54 29-314 ( > '\2\ 4 -6S7 346 91 4S 679 ■590 Mount I)rS(.-rl 5 26 36 -.SgS f " "337 37 235 0-129 4 '3'' 343 ^^4 '3 75' -296 r.iirki- 160 5« 42 ■36" 1 051 41 -31 H^ - 1 29 4 ■674 354 i" 47 244 ■■9'^ I'.ppiiiL; l'",;ist I!,- sc '3 34 42 -.(ex. "■557 1 1 843 - 1 29 4 -531 S7S92 34031 3-^' * .Miuiiil IH-si'il -3 '7 01 756 ■26.S 01 -4S,s "■532 4 •322 77'^ •'^^ 21 027 ■••72 'I'uiik '17 21 33 '9'" 294 33-616 "'533 4 -674 354 ... 47 24- J ■79'> Mpliini; Ivisl B: sc 39 21 25 MSo ■ 1 •»3 4 26 -494 ' ' 533 4 -52S .*s 3^1 33 733 •.V.7 Mount Dc-scrl 25 10 22 -4X7 \ i> 45 " 22 -938 ..•496 4 >'^4 325 57 24 22s 3m lvi)piiiK Iv'sl Kasi- 3" 52 CX) •20() 1 •S7S m -078 0-496 4 '4'^5 73' 76 29 223 ■4'>'' Pivji'ou '23 57 37 170 1 i»\V>3 37 "473 0-497 -i -674 354 ... 47 244 T-^"^ Mount lk-S(.-rl 32 1(1 26 •4S2 u '1)62 2(1 •420 1 231 4S.) 32.) 43 30 855 27'^ lhuii|)1)ai-k 54 5*' 40 476 t -hi;. 41 lU) 1 23 1 •'■'74 354 '•• 47 244 T"-*" I'lppiuL; Ivast \\\ sc 92 52 5'>'3ii' "■"57 5'' 153 1 -230 761 26S 03 57 7»2 253 Momil Drsi-il '7 5'> 24-S5S ^ii.S 24 253 0-297 -021 6f>2 33 u> 51 1 443 'I'mik Sj 4>' 56 070 ■ '65 1 5'' 721 -29: 53 ' ■'^7^ 93 34 031 ■33-^^ llnik> 79 jS 39 "50 I I) •76,S 39 '9 1 >> o-2v)S -52S .<)5 3ti 33 733 •S07 Mount DosiTl 3" 3'' 59 w^s ; •7SS 60 -173 0-42S -23S S47 M '7 33" 957 I'.uikr 59 10 22 •54(^ 1145 i^ 495 0-42S ■4*^5 731 ~'^ 2^) 223 \f^^ rii;<.'oti i)<) 1 2 ;,S-i4>' 470 3S -b 1 (> 0-42S -531 S:s g." 34 03 1 -vV* 3S THE EASTERN OBLIQUE ARC. 28 29 n 34 35 36 37 3« /\esnlli>!g aiiiiU's and sides of the lipping Correc- basc uii , Maine — continued. iNIount Desert Humpback Burke Mount Desert Tunk Pigeon Mount Desert Humpback Tunk Mount ] )esert Humpback Pigeon Howard Burke Epping East Base Howard Pigeon Epping Blast Base Howard Pipping East Base Humpback Howard Mount Desert Pipping East Base Howard Pigeon Burke Howard P.urke Humpback Ho want Mount Desert Burke Howard Pigeon Humpback ( )bscrvcd ansrles. 26 49 123 48 56 74 19 27 43 49 02 8 12 59 24 " 39 I5« 48 55 26 48 23 53 ''9 19 28 06 19 45 57 30 92 1 1 30 I3-' 92 4 '663 658 76 4 -863 228 98 4 '687 346 91 4 -794 490 44 4 '641 374 53 Distance in meters. 31 363 -129 34 03 1 -330 57 712 -253 26 161 -352 29 223 -468 33 733 •■'^07 24 955 '954 33 733 '807 57 712 -253 48 679 -590 29 223 -468 57 712-253 13 751 '296 34 923 -483 46 095 -524 24 228 -390 34 923 -482 43 789 '958 30 855 -276 62 300 -345 34 923 '482 47 244 798 34 923 -4S2 72 984 -221 17 331 '957 46 095 -523 43 789 '958 31 363-129 62 300 -346 46 095 -524 34 03 1 -330 46 095 -524 72 984 -221 48 679 -590 62 300. 345 43 789 '958 No. 39 4' 42 43 44 45 46 I'.ASl', IJNES AND JJASK Nl-.TS. A't's/{/////i; (r//L;//s lu/i/ M'(/ts nf Ihc /■'.ppiin; /nise iii-/ , Maim — roiilimicfl itioiis ObsL-rvcd Miii^lcs. 39 t_asr t/>//\ .1/assar///(srtts. /,sv/. This base was the third and last one measured with the Hassler ba.se apparatus and followed within a few months the measure of the Kent Island ba.se. Its site is on the Boston and Providence Railroad, in Bristol County, Massachusetts, and about 12 kilo- meters (7)^ statute miles) to the northward and eastward of Providence, Rliode Island. An account of this base is given in the Coast Survey Report for 1865, Appendix Xo. 21, page 189, and little need be .said here respecting the apparatus, a description of which can be found in the account of the measurement of the Fire Island and Kent Island bases. Its middle point is in latitude 4i°'58'"9 and in longitude 71° is''3< the mean azimuth is 27° 49'"2, and its length 17?^ kilometers (or nearly 10^ .statute miles ). There are Intt two bases in the United States (both in California) which exceed this length. The line was measured by A.ssistant Edmund Blunt during September, October, and November, 1844. As in the case of the two bases previously measured by the Sur\-e\-, but one measure was made. The length adopted for the compound S-meter bar rests upon the comparisons of 1844-45, with the resulting length of 7'999 8716 meters at o C. ± 55 (see account of the Kent I.sland lia.se). Tlie mean temperature of the bar during the mea.surement was 14° '92 C. (or 58° '85 F. ); the average elevation of the apparatus above the half-tide level at Boston Harbor was 44'" "83. The record at this ba.se is defi- cient in details. The resulting length of the base is as follows: 2 165 bo.xes 17 3i9'"'722i Correction for exccs.s of teiiipiTaturi' -j- 3'23S3 Correction for inclination — o's^^g Fractional part of a box at Northea.'^t Base + 3 9999 Correction for 10° difference of teinperatnre for above — o"ocxj3 Additional lenf>th measured by scale -r OM012 Reduction to lialf-tide level — o"i22o Resulting lenglli of base 17 326"''376^ 4: THE EASTERN (~)BLIOUE ARC. To form an estimate of the accuracy of this measure, we find, from the probable error assigned to the base bars, that of the base to be d= o"''oi 19. With reference to tempera- ture, 702 boxes were laid with rising and 579 with falling temperature, and for the rest of the boxes the temperature was stationary. The assumed probable error from this con- dition and probable lag, and from gradtiation error is zbo'"'0332, and the probable error from instability of the microscopes is taken as =bo"''oo59. Combining these three independent values, we get for tlie probable error of the base d= o'" '0358, which equals We have, therefore, the final result for the length of the 4 8 3^80 oi its length Ma,s.sachusetts base 17 326'3763 meters, and its logarithm 4'23.S 70774. ± •035« ± 90. No. 5. BLwe JIM 'Jlic con)u:ctio)i of the Massacliusctts base ~n'ith tlic Diaiii triaiiff illation . The Ma.s.sacliusetts base is connected with the main triangulation in an unusual way — that is, with a ba.se net so simple as to render a .special adju.stment of it unnece.ssary. The conditional equations, therefore, which sub.si.st between the three northern base lines were extended to reach directly to the Mas;:achusetts base without any interven- tion of a .special ba.se net adjustment. The diagram shows the direct con- nection of the ba.se with the triangtila- tion of the New England States, the quadrilateral Beacon Pole, Copectit, Manomet, and Blue Hill being an integral part thereof. One advantage which the base po.s,ses.ses over the other two is its great length. The following table gives the ap- ])roximate elevation above the Atlantic (if tile stati(jns adjacent to the base: Meters. Feet. Ma.s.sachusetts vSoutli Base 33 108 MassachiLsetts North Base 70 23 1 Beacon Pole 167 548 Great Meadow .So's 264 Copecut 107-5 353 Maiioniet 1 20 394 Blue Hill 194 635 rCopccut Statut* Miles 10 O 10 Kilometers 20 10 10 20 30 40 Di'scriptioits of stotioiis. The descriptions of these old stations are very meager. The following information is all that could be gathered: J/assac/iKSt'tts Soitt/i Base, /(Vy/. — The station is located on the Boston and Pro\-idence Railroad, in Bristol Countw Ma.ssachu.setts. For a ground mark a stone of the follow- ing dimensions was buried: Length, 4 feet 7 >4 inches; base, 12 inches square; top, 6 inches square. A copper bolt, on which there is a cro.ss mark ( + ), driven in t^^e stone defines tile starting point of the measure. The stone is S feet from the ea.stern rail of the Boston and Trox-idence Railroad, there Ijeing but one track laid. " .Another stone is placed I BASH LINES AND BASE NETS. 43 oil the west side of the road in the hue toward ]5eaconpole Hill, 6 inches heinj^ above gnnind, and distant 33 feet from the termination of the base." * Massachusetts North Base, 18^^. — The station is marked hy a Ijrick tower, stated by G. Bradford to be 44 feet in height, when reoccupied October 18, 1884. The center of the station is indicated by a brass Ixjlt in the center of a stone, thus + . It is central with the tower. The cap .stone (of 1844) had a mean diameter of o'32 meter. Bcaconpole, 184^. — This statical is located al)out 2 miles northeasterly from the village of Cumberland Hill. The station was visited and reoccupied in vSeptemlx;r, 1884, by Assistant G. Bradford, who remarks: "Found here, guided by K. H. Pickering, an old resident, a copper (brass?) bolt set in lead and filling a hole drilled in a ledge of rock .some 30 feet in diameter, which occupies the summit of the elevation." A tripod signal was built over the station in 1884. There is also a description of 1896 by H. B. Wood, of the " vSurvey of the Commonwealth of Mas.sachusetts. " Copecut, 1S44. — Station on Copecut Hill between Fall River and New Bedford. As.sist- ant G. Bradford found here in November, 1884, a copper bolt in a rock, presumably the center of the station. A large pile of stones was found about the bolt, covering it. The place is surrounded with bushes and small trees, and is difficult to find without a guide. The road to it through the woods is extremely rough. A tripod signal was built here in 1884. Great Mcadozc, 184J. — This is one of the Borden Survey stations; about 3 miles north of west of Rehoboth village, 7 miles from Taunton, and 12 from Providence, Rhode Island. A.ssi.stant G. Bradford, in September, 1884, found here a hole in the rock, where, an old resident says, the signal once stood. The trees have grown up, and are now to the northward and westward some 40 to 50 feet high. The following descrip- tion is by Assistant C. H. Van Orden, in i88g: 'The hill is well known and is called Great Meadow Hill by the people about North Rehoboth. It is best approached from the south side. It is a large flat hill, with a growth of timber on the east and west sides. Directly north of the station is an open lot or meadow, noticeable from a di.stance." Manomct, 18-I.5. — Near Plymouth, Ma.ssachu.setts. A.ssistant C. O. Boutelle states, in his record of the latitude observations of July, 1867: " The triangulation .station at Manomet has been more permanently marked l)y drilling three holes, forming an equi- lateral triangle around the copper bolt, and each hole is distant 6 inches from it. The two holes south of the bolt are east and west from each other antl the third hole is north from the bolt. Each hole is five-eighths of an inch in diameter and 2 inches deep." In September, 1877, Assistant G. A. Fairfield writes: "Visited this .station and found it undisturbed; had no difficulty in finding the rock with copper bolt and three drill holes. Blue Hill, i^-l-S- — Near Dedham, Massachusetts. The Coast Survey station is distant from the Borden survey .station of Blue Hill 8^337 meters, and the azimuth of the Borden .station is 11° 16', as deduced from computation of December, 18S4. The Borden station was located in the middle of a .square inclosure of stones. In November. 1886, A.ssistant C. H. ^'an Orden visited the station and found the Coast Survey copper bolt (outside the old Borden inclosure) in gooil order. Borden's " Blue Hill" is under the stone tower of the " Blue Hill Observatory. " The private meteorological ob.servatory at this place was e.stablished by Mr. A. L. Rotch in 1885. It is a two-story circular tower, 12 feet in diameter in.side and 25 feel high, l)uilt of the l)roken stone fmind on llie liill. I'!xtending southward from this * l-roin original rcionl ol the hasc iiicasurt nutil. 44 I'HE EASTERN OBLIQUE ARC. tower is a one-story, hip-roof liouse, built of stone, with a wooden shed attached. (See heUotype in Annals of the Astronomical Observatorj' of Harvard College, Volume XX, Cambridge, 1896). There is also a description of 1896 by H. B. Wood of the "Survey of the Commonwealth of Massachusetts. ' ' A sketch shows the Coast vSurx'ey station with reference to the tower. 3. THK FIKK ISLAND BASE LINE AND BASE NET, NEW YORK, 1834. /vocation, vicasuriinoii, a?id >rsii/thig /oigt/i of the Fire Island Base Line, New York, i8jif. The site of this base is on the southern shore of Long Island, New York, on the narrow Fire Island beach between the Great South Bay and the Atlantic Ocean, and distant nearly So kilometers, or 50 statute miles, to the east from New York City. It was the first and only primary base measured bj' Superintendent F. R. Has.sler, and the measurement was made with an apparatus of his own design. He has left a full descrip- tion, with illustrations, in detail, of this apparatus in the Transactions of the American Philosophical Society, Philadelphia, Pennsylvania, new series, 1825, Volume II, pages 273-2S6. The essential parts of the apparatus are enumerated in No. 12 of his cata- logue of instruments, which probably dates back to the year 18 16. These parts appear to have been made by Troughton, of London, in 18 13. Two other primary base lines were measured with the same apparatus, viz, the Kent Island and the Massachusetts bases. The beach over which the measure extended is sandy, interspersed with low hum- mocks and ridges, and subject to changes from storms, which caused the west end of the base to be finalh* lost, notwithstanding a strong timber protection surrounded the hillock. The eastern terminal point was further removed from the beach, which caused a bend in the line close to the monument, and necessitated the measure of an angle at the bend. The insecurity of this exposed base and the danger of its loss caused the transfer of its length, a few years later, to be made to a primary line located on the central hills of Long Lsland. The base net, therefore, in this case consists simph' of a quadrilateral. The length of the base is about 14 kilometers (or 8% statute miles). The central point is in latitude 40° 38' '9, and in longitude 73° o8''i. The mean of the forward and backward azimv;ths is 72° 56' '8. For convenience of reference, a brief description of the Hassler base apparatus is repeated here from his description, and further remarks on this subject will be found in connection with the Kent Island base. It makes use of one measuring bar and of optical contact. The bar is 8 meters in length and is composed of four 2-meter iron bars placed in contact lengthwise. These pieces are of square section * and are firmly held together l).v means of collars clamped over the bar ends and bringing them together by means of .screw bolts. The whole or compound bar is supported on 15 rollers, resting on a wooden beam, itself adjustable upon another similar support. The whole is placed in the bottom of a wooden trough. There are eight thermometers, two placed on the upper surface of each of the single bars to ascertain their temperature. A sector for measuring the inclination is attached to one end of the supporting beam, and all required mechanical appliances for the adjustment and alignment of the bar, as well as for the manipulation of the micrometer micro- scopes, are provided. The trough itself rests upon five trestles. The two microscopes are likewise mounted upon trestles. For alignment of the base the trough or box carries at one end a small telescope and at the opposite end a short vertical pin to *The same as that of the Committee Meter, FERDINAND RUDOLPH HASSLER (1770 1843). HASH ijnp:s and hasp: nets. 45 define the axis of the apparatus and the direction of the Hne of measure. The micro- scopes admit of adjustment for verticahty of axis. Their objectives are composed of two half lenses of different foci, one ior pointing on spider tlireads stretched across small central half-circular notches cut vertically into the end faces of the protrudinj( measuring bar, the other focus serving for a verification of the steadiness of the optical axis, the pointing being made upon cross lines ruled on an ivory ])late resting ou the support below the microscope. For the standardization (jf the measuring bar repeated comparisons were made at difTerent times by different ol)servers and by different means. The Hassler double end- meters, known as bars A, B, C, and I), were first compared in Februar\' and March, isiy, with the Committee Meter and a .standardized iron a bout meter by Lenoir. In the same year Hassler determined their coefficient of expansion and found it o'ooo 006 963 for Fahrenheit's scale or o'ooo 012 534 for the Centigrade scale, a value somewhat large \et probably applying to these particular bars, but this could not l)e verified, the bars having long since been lost. In May, 1S34, and March, 1835, in connection with the Fire Island ba.se, comparisons were made involving the Troughton brass scale and the Connnittee Meter. The last compari.sons date from 1 844-45 , and were made with a Bessel level-contact comparator, using the Lenoir iron meter. The results were, for the combined lengtli ato°C: From coniparison.s of 1S17 2 = 7"''999 9506 From comparisons of 1S34-35 8"ooo 0414* ± 242 FVoni compari-soiis of 1S44-45 7 '999 >'^7i6 r+T 55 When the comparisons in 1835 in connection with the Fire Island base had l)een made an examination of bars A and B showed them to be rusty. After cleaning them they were again com- ^. _ ^ pared, and the new 1835 value ^= 7"'"999 9764 re- sulted. The last ob.ser- vations indicate a decided apparent shortening, which has not been ac- cotinted for satisfactorily except it be due to the manner in which the 8-meter bar was built up. Upon the whole, it has been thought best to adopt the Has.sler value of 1834-35 for the reduc- tion of the Fire Island base as representing the conditions then existing. But one measure of the base was made, owing probably to the labor and time required to measure such a long line. The measure was made during the months of August, September, and October, 1834. The above diagram shows the condition at East Monument U *The v.iltif fdiiiul in odntiectioti with the Kire Islaiul txise. 46 THE EASTERN OBLIQUE ARC. the eastern end. The distances 2 to 3, 3 to 4, and 4 to 5 were measured with the base apparatus, and the angular horizontal directions of the fine and heavy lines at the points I, 2, 3, 4, and 5 were obtained by means of a theodolite. Calling" West Ba.se No. 6, the points 6, 5, 4, and 3 were placed in line. For reduction of the measured length of the base to sea level, the average height of the bar above the half -tide level of the Atlantic was taken as 2 '75 meters. The mean temperature of the bar during measurement was 26° '60 C. (or 79° '90 F. ). The resulting length from West Ba.se to East End was as follows: I 725 boxes 13 800"^ '07 14 Correction for excess of temperature over o°C + 4'6o3i Correction for inclination — 0'2055 Reduction to half-tide level of ocean — o'oo6o Resulting length 13 So^""4630 Similarly we have the short measures at the eastern end. Line measured 2 to 3 5 to 4 3 to 4 Number of boxes 14 17 7 Corre.sponding length ii2"''ooo6 I36"''ooo7 56""ooo3 Correction for expan.sion -fo'02i6 ^o"0276 -j-o'cirg Correction for inclination — o'o65o — o'o268 — 0*0038 Defect of last bo.x at eastern end -f'0'8203 4-i'i38o Resulting length H2"'7775 i36'"-ooi5 57'"T464 In the adjustmewt of the linear and angitlar mea.stu'es, it has lieen a.sstuned that the former require no correction; the figure adjustment of i, 2, 3, 4, and 5 involves two angle, two side, and two distance or length equations,* and the resulting length for line 5 to 1 was 294'752 meters. If West Ba.se l)e designated as 6, then by the known dis- tances 6 to 5 and i to 5 and the known angles, the angle at 6 between East F^nd and East Base is found equal to 36' 41" '3, whence the final length We,st Ba,se to East Base l)ecomes 14 05.S'g709 meters and its logarithm 4' 147 953 53. To ascertain the probable error of this result, we estimate that of the line 6 to 5 as d=o""oooo242 for each box, hence for thewhole di.stance ±o""o4i7. Respecting the tem- perature of the bar, 455 boxes being placed with rising temperatttre, 553 with .stationary temperature, and 717 with falling temperature, and a.s.suming a po,s.sible error in temper- ature of 2°, the probable error of the base might be it o"''029. The effect of the gradu- ation error is estimated at d=o"''023 or ±o"'"037o for combined effect. The probable error arising from instability of microscopes was assumed to be±o""ooo 127 and the total effect d= o'"'oo53. These are the principal .sources of error and when combined produce ±:o"''057 for the line 6 to 5. To obtain the probable error for the line between the monuments =ho"''oi3 was added, hence the probable error of the base as e.stimated is v/(o-o57)'+ (o-oi3)^ = ±o""o585. This equals — part of the whole length, the corresponding \-altie \n the loga- rithm of the length =t -, — = o '000 001 807. Consequently, the final result for the 1 .1 f.i T7- Ti lu • 14058-9709 4'i47 953 53 length or the Frre Island ba.se rs , ,, meters, arrd rts logarrthm , ,, '' zt 0585 ' ± I 8r ♦All measures involved in this adjustment were found satisfactory. HASIv LINKS AND liASK NKTS. 47 Thr l-iit hidiid base net and ycsitlls of its adjuslnicnl. In this net we iiu-liuk- llie (iiiadrilateral whicli transfers tlie measured hase to the so-called mountain base, and the two other quadrilaterals, one within the other, which start from this derived l)ase. The line Wooster to Sandford will he the connecting link with the northeastern trian^ulation, and the line West ^^ - Hills to Bald Hill will form the link for tlie soutli western l)ranch. The elevations of the stations ahoNx- the sea le\-el are verj- moderate and the horizontal directions needed but very small corrections, the maxinunn bein^^ less than o"'o2, but no account of this was taken when less than o"oo3. The approximate hei = i/{e\-\-e'J. Among the values of e^ there was one exceptionally large, and, omitting it, we find t'^ = ± o""i8, hence e^ =V(o'233)° — (o'lSs)" = =b o' i44and/i = 1/ [( o"i44)'+ (',,'] . and in order to make the average sum of the recip- rocals of the weights nearly unity, the values of i/p were multiplied by 13. The range in these relative weights is still -large, the ratio of the greatest to the least being as 16 to I, but it would have been as 144 to i had not the equalizing device been introduced. Comparing the old with the present results they are found to be nearly the same. For the side Wooster to vSandford we have old log. distance ( Coast Survey Report for 1865, pages 201-202) 4"669 171 i and by the present adju.stment 4-669 171 o, which log. difference corresponds to a linear difference of but 2 centimeters. For the side Bald Hill to West Hills we have old log. di.stance ( Coa.st Survey Report for 1866, page 52) 4-648 135 3, and by the present adjustment 4-648 135 6, corresponding to a linear difference of 4 centimeters. A preliminary publication of results of the triangulation about this ba.se and vicinity was made in 185 1 in the Coast Survey Report of that date, pages 222 and following. A second publication will be found in the Coast Survey Report for 1865, pages 201-202. These results are now superseded. Abstracts of horizontal directions at stations formimr the Fire Island lUxse Net. /Sjj-/S6_). Fire Island East Base, Suffolk County, New York. October i to October 8, 1S37. F. R. Has,sler, observer. 75*-"' ilirection theodolite No. i. Circle used in V! positions. No. of ilirectioiis- 4'S 95 57 47 -652 o'oS —0 -009 47 '643 -f-O -285 47 •928 124 51 45 '93^ -08 ^0 -005 45 -943 154 10 3S -493 -07 -0-I47 38 -378 Bald Hill, Fairfield Cotinty, Connectictit. + o "032 July 23 to August 18, 1833. I'. R. Hassler, observer. 60'"' direction theodolite No. 2. Circle used in VI positions. 34 Tashua 35 Ruland 36 West Hills Harrow Round Hill I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI o 00 62 40 99 31 121 42 15S 36 00 000 12 '802 - o-o56t 40 -835 1 8 '609 54 "002 =hO '22 O '60 0-27 0-19 o '40 o •006 00 006 -0103 59-903 -^1-433 14-291 —0-213 40-622 FIRK ISLAND li.ASF, NF/f. Observation equations. o=+o-945- (i)f (3)~- {A)+ (5)-(i9) + (2o) o=-o-i58- (2)+ (3)- (4)+ (6)- (7)+ (S) 0=^-0-027- (i)+ (2) - (S)+ (9)-(iS) + (2o) 0= -f 0-462- ( 15) + ( 17 ) - ( 22 ) + ( 24) - - ( 25 ) + ( 28) o=-o-9S8- (9) + (i3)-(i7) + (i8)-(2i) + (22) o=+o-32i-- (9)f(ii)-^(i5) + (iS)-(27)-+-(28) 0=-0-236~(l2)-f (l3)-(2l) + (23)-(29)^(30) o=+o-o72--(i6) + (iS) (9) + (;i2)-(3o) + (3i) o= + i-026-(i5) + (i6) (26) + (28)^-(3i) + (33) o=:-<-o-o93.-(r4) + (i6)-(3i) + (32) -(34)-f(36) o= + i-432-(i4)-| (iS)-- (9) + (io)-(35) + (36) o=~9"5 + 2-99(4) -2-12(5) -0-87(6)4-4-08(7) -5-74(8) -I -66(9) 4- 1 -49( iSV-5-3S( i9)-3-S9(2o) o=+4-2+i-56(9)-]-i4(ii)-o-42(i3)+4-S7(2i)-6-92(22)-2-o5(24) -0-38(25^-3-75(27^ +4-13(28) o=+3-o+o-6o(9) -4'68( i2)-f 4-o8(i3)+8-7i(i6) -9-58( 17 )-• 2-29^21 ) 6-o5(22)-3-76u3l +0-871 iSi o=—o-8 1-0-60(9) 9'46(ii ) +8-86(1 2)4 5-32(15) 6-i9( i6)+o-S7( iS) -2-5u 26) -3-821 27) + 1-31(28) o= + i-44-i-57(9)-7-i3(io) t 5'56(i2l 5-15(14) -5-i5( 16) -i-o-oo( iS^ 0-24^30) -1-30(31) + 1-54(32^ ♦Correction for eccentricilv indicated. t Correction to refer the old to the new stntion of 1865. 52 THE EASTERN OBLIQUE ARC. Reciprocals of the iveights or -calues of ^3 0= +0-945 o = — o'i58 0=+0'027 o=+o'462 0= -0-988 o = + o-32i o=— 0-236 0= +0-072 = + 1-026 0= +0-093 0= + 1-432 o=-9'5 o=+4-2 o=+3'o o=— 0-8 o= + i-4 C2 0-9 1-6 I '4 '•4 07 0-5 0-9 19 9-4 +3'0 +3'3 6-0 —I -8 8-6 10 n 12 13 14 15 16 17 iS 1-2 0-4 0-3 0-4 I 'I 0-3 0-3 0-4 1-6 19 20 21 22 22 24 25 26 27 17 2-1 0-4 0-5 0-5 ro o"3 0-4 0-4 C3 C4 C5 C6 Normal equations. C7 Cg C9 Cio Cii Cn 28 0-3 29 0-3 30 0-4 31 0-4 32 2-8 33 0-3 34 0-9 35 4-9 36 1-2 Cm C15 -35 -35 -3'5 —0-9 +0-6 +0-6 5-2 +3-5 +0-8 +3-5 4'9 +3'5 +0'6 2-3 -0-7 4-9 -0-7 -0-7 2-0 +0-7 6-7 C, = — o -4899 Cj= +0-5886 C3= +0-1590 C4 = +o -2016 -3'5 + 3-5 +3'5 + 2-3 11-9 + io-i6i — 12-001 + 14-105 — 0*770 - 0-770 - 0770 — 0-770 147-085 + 2 964 +6-863 -S-540 -0-681 — 2-116 -2-964 + 1-239 +4 920 53 '630 Resulting values of correlates. C5 = -ri '1956 C6 = -o-i55o C7=--o-3553 C8= -0-5471 C -o -8014 C,o=+o-ii45 C,i = --o -2924 C,^=+o-i348 - 0252 - 0-S07 + ■■"75 + 0-252 + 4-000 - 3765 + 2-613 + 2-613 + 0-252 + 3-966 + 26-4S7 I02-o6l - 0-252 - 1-203 + 0-252 - 3-207 - 2-658 -t- 4-767 — 4-064 - 1-857 + 0-252 + 3-966 + I3-'145 -26-719 90' 100 C„= +0-0750 Ci4 = — 0-0807 C,5 = — 0-0361 C,6= —0-0563 C16 + 2-983 - 2-983 - 2-983 - 1-764- - 0-194 - 1-025 - 2-378 - 17-204 + 4-951 ■^ 4-653 -19-473 + 26-132 119-437 Resulting corrections to observed directions. (l) = = +0-397 (io) = = +0-131 (19) = = —0 -400 (28) = = —0-148 Probable error of (2) -0 -387 (II) +0 -040 (20) +0 -406 (29) + 0-107 an observed direc- (3) +0-158 +0 -426 - 1 -086 (12) (13) (14) -0-134 -|-o -192 — O-T23 (21) (22) (23) —0 -264 +0 -482 -0 -329 (30) (31) (32) + -082 + -085 + -078 tion. (4) (5) -■^"V'tT (6) ^0-330 (15) + 0-169 (24) + -355 (33) — -240 " (7) ~o -019 (16) -0 '099 (25) —0 -069 (34) -0-103 = ±0-34 (8) -0-310 (17) -0 -089 (26) +0 -284 (35) + ' '433 (9) +0 -266 (18) +0 -226 (27) + 0-005 (36) —0-214 Check: -VwQA =4-133 and [ pVvl^A ■I35- BASE LINES AND BASE NETS. 53 Ucsul/in if u>i}^/('s and side sn/(/ic /' iff fslavd base ncl. No. Stations. Ob.served angles. Correc- tioti. Spher- ical aiiKles. exceL. I-""- Distances iti meters. / // // /' // - 7+ 8 Rulaiid 27 J 7 02716 290 02 -426 -218 4-147 953 5 14 058-971 - 4+ 6 Fire Island East Ba.se 112 32 52 425 -0 096 52 -329 -217 4-452 173 4 28 325 23 - 2+ 3 Fire Island West Base 40 1" 05-353 H-0 -544 05 -897 0-217 4-296 291 [ 19 782 -95 -19+20 West Hills 21 21 45' 133 po -806 45 939 -296 (•'47 953 5 14 058-971 ■ 4+ 5 Fire Island East Base 44 48 25 • 1 29 I -512 23 -617 0296 4 -434 543 27 198-38 - '+ 3 Fire Island West Base "3 49 5 J '571 0-239 51 -332 0296 4 -547 828 6 35 304 -38 -18+20 West Hills 54 43 : 6 '067 jo -180 :6 -247 -026 4-452 173 4 28 325 23 - 8+ 9 Rnland 51 36 59-619 +0 -576 60-195 -625 4 -434 543 27 198-38 - 1+ 2 Fire Island West Base 73 39 46-218 -0 -783 45 '435 -626 4-522 397 2 33 296-39 -1S+19 We,st Hills 33 2 1 30 '934 -0 -626 30 -308 0-547 4 -296 291 1 19 782-95 - 7+ 9 Rnland 7« 54 02 -335 t-o -286 02 -62 1 0-547 4 -547 828 5 35 304 -37 - 5+ 6 Fire Island East Base 67 44 27 -296 (-1 -416 28 -712 0-547 4 -522 397 1 33 296-39 ■30+31 Tashua 3'^ 20 42-545 +0 -003 42 -548 I -344 4 -522 397 1 33 296 -39 9+12 Ruland 73 59 43 '301 —0 -400 42 -901 ' -345 4 ■7>2 561 3 51 589 50 -16+1S West Hills 67 39 38 -259 +0 -325 38 -584 I -344 4 -695 847 6 49 641 -Si -27-t-28 Wooster 29 'S 52-587 —0-152 52 •4.^,5 • -683 4-522 397 1 33 296-39 9+II Ruland 6[ 26 28 -038 —0 -226 27-812 1-683 4 -776 212 I 59 732 -69 15+18 West Hills 89 14 44-744 +0 -057 44 -' Assistant Farley in 1868, who found fragments of an earthenware crock (of the pattern of the Hassler crocks, or cones, as he called them), and marks cut on three rocks, but he was not able to identify the marks owing to the (apparent ) loss of the original description of the station by vSuperintendent Hassler and by As.sistant Blunt in i.s6ri. Wliat made the search at the place more difficult was the fact that rock blasting- had Ijcen going on there for .some time. A second visit in 1869 elicited no certain information from want of application of proper means. The place was next examined 1)\' Assistant G. Bradford in 1882 and 1SS4, when, 1)}- means of the determination of a temporary signal, the location of the crock (cone) placed bj' Assistant Blunt in 1866 was readily discovered. It is a.ssunied that this crock occupies the position of the Hassler crock, because A.ssistant Blunt is said to have put it in the place of the fragments of the older one. The station appears to have been recovered. ]\\iostci\ Fairfield County, Connecticut. This station was e.stal)lished in 1864 by the party of vSuperintendent Bache. It is located in Ridgefield Township, about 4 miles .southwest of Danbury, on Wooster Mountain, known to the residents in the vicinity as Pine Hill. The station point is marked b}' a copper bolt, and is located on the highest point of gneiss which crops out near the summit of the mountain. The top of the ledge is quite limited, its length east and west being about 25 feet. 4. THK KENT ISLAND BA.SK LINE, BASE NET AND EXTEN.SION, JNLVRVLAND, 1 844. Louitioit . iiHasiD'inuiit . iDid rcsu/fiiig Ic/igjh of ^'^^ Kent Island base line, Maryland, /S/^. Kent Island, in Queen Anne County, Maryland, on the western shore of which the base was measured, is situated on the east .side of Chesapeake Bay, and is nearly oppo- .site Annapolis Harl>or. Originally it was intended as a check on the main triangvilation which extended from the Fire Island ba.se .southward and westward, but its po.sition near the latitude of 39" rendered it desirable to incorporate it in the ea.stern part of the transcontinental triangulation. An account of the measure and length of this base is contained in the Coast Survey Report for the year 1866, supplement to Appendix No. 8, page 140, and again in Special Publication No. 4, "The Transcontinental Triangulation." The middle point of the Ijase is in latitude 38° 56'' i, and in longitude 76° 2i''2, the mean a/.inuith is 14° 35''4, and the length 87 kilometers (or 5'4 statute miles). The surface of this part of the i.sland is slightly undulating, and the line crosses cultivated fields, with some portions covered by swamps and woods. The elevation is verj- little above the surface of the bay. The shore is subject to erosion, in consequence of which the terminal monuments, each consisting of an upright .stone surface mark with a copper BASE LINES AND HASE NETS. 57 bolt in a piece of slate below the surface, the whole being protected by nibble masonry, have disappeared. The base was measured I)}' Assistant J. Ferguson, in .Ma\' aiul June, 1844. by means of the same apparatus as was used for the measure of the Fire Island base ten years before. It is known as the Hasslerba.se apparatus,* and consists oi four rectangu- lar iron bars eacli 2 meters long, put together endwise and aligned in a wooden trough. The protruding ends of this S-meter 1)ar ha\-e semicircular notches f ' ■'™^ acnws which was stretched a spider thread; over this was mounted, f '^ on an independent stand, an adjustaljle micrometer microscope, b\- means of which tlie mea.sure was held while the l)ar was brought forward into a new position. All needed adjust- ments for the apparatus were provided for and the temperature of the bar was read from thermometers attached to the top of the 2-meter bars placed in the liottom of the trough, 1; which is .supposed to have been covered with canvas. At the end oi a day's work or at other times when neces.sary, the end of the last bar laid was transferred to the ground, generally by a plummet. Only one measure was made, and the total time cf)nsumed was a little over one month. The four 2-meter bars made by Troughton, of London, about 18 13 were standardized in 1817 by Hassler, by using the Committee Meter, in 1834-35 by using the Troughton bra.ss .scale, and finally, in 1844-45, b}' Superintendent Bache. J. Sa.xton, and \V. Wiirdemann, by u.sing a Bessel comparator, with the following results: 111 ISI7 ■2' = 7""999 9506 at 0° C 1834-35 S 'ooo 0414 1835 t7-999 9764 IS44-45 7-999 S716 ± 5,5 This last value, after verification in July, 1854, was finally adopted for the two bases measured with this apparatus in 1S44. The coefficient of expansion of the bar which was determined in 18 17 by Ha.ssler at Newark, viz, o'ooo 012 534 for the centigrade scale, was adopted and, though somewhat large, may nevertheless be true for these particular bars, now lost. The mean temperature of the bar during measurement of the base was 25°"i8 C. (or 77°'33 F.). The deduced length of the base is as follows: I 0S6 boxes .S6S7"'-,S6o6 Excess of last box over end mark at South Rase, as measured b%- Bar D and .scaK- 2 '0508 Correction for excess (25° 44 C.) of temperature of bars over 0° C. and graduation error of thermometers ( — o°'255 C. ) -2 7424 Correction for inclination of boxes 1 \xx17 Redviction to half-tide level of bay for surface elevation and height of boxes 5"''o — 0*0069 Resulting length of base S6S7"'5446 The probal)le error of this value can (ml\- be estimated, since the base was meas- ured but once. Supposing the combined length of the four 2-meter bars subject to ±20/i, the effect on the ba.se will be ±o"'"o22; an assiuned error of ±5',, part in the *Kor a description, with illustrations, of the apparatus, seethe Transactions of the .\raerican Philosophicil Society, Philadelphia, Pennsylvania, for the year iSj5, pp. 27,viJ*fi. ."^ee also the preceding: account of the I'irc Island Ivase nieasnrotuent, tRes\iU of coniparison>. uuule :ifter cleanitii; two of the J-iueler hats which were louiul ruslv when examined. 58 THK EASTERN OBLIQUE ARC. coefficient of expansion would produce dr o'""055; again, the effect for imperfect tempera- ture correction, for inequality in number of boxes laid with rising and with falling temperatures, may be taken as d=o"''034; other minor uncertainties may be omitted. Combining the several values for probable error gives zho'"'o68, equal to 27^00 of the length nearh'. This ma}' be taken to represent the measuring error, and to include the probable error due to our practical unit of length, the Committee Meter, taken as ± Hm- Resulting length of Kent Island base, S 687'5446 meters and its logarithm, ±■0680 3-938 8 97 05 ±3 40 A'(7// Is/aitd /hisr net and restills of adjiisluutii. The following abstracts of observed and adjusted directions at the nine stations form- ing the base net proper, as well as the conditional equations and results of its adjustment with resulting length of triangle sides, were copied from Part I, Special Publication No. 4, " The Transcontinental Triangulation," and from Part III of the same publication the results of two triangles * to the northward of the net and of 35 triangles to the westward and southward of the base.t The triangles of this last extension are shown on the foUow- inof sketch: OsbornesRuirt Finlay Kent Island North Base Kent Island South Base Marriott Kilometers Statute Miles 10 * Shown on the above sketch by dotted lines. tFor adjustment of this work see Special Publication No. 4, ■ The Transcontinental Triangulation.' BASE LINES AND BASE NETS. 59 The heights of the stations above the half-tide level of the ocean are small and approximately as follows: Meiers Kent Island North Base 5 Kent Island South Base 5 Taylor 29 Marriott 76 Linstid 48 Webb 72 Swan 8 Pooles Island 4 Finlay 150 Osbornes Ruin 90 Turkey Point 25 f stations along the Blue K Meters. Hill 84 ■ Soper 143 Stabler 174 Peach Grove 159 Sugar Loaf 390 Maryland Heights 444 Bull Run 419 Mount Marshall 028 Fork 174 Clark 334 Humpback i no Spear 492 Tobacco Row 895 No corrections to the observed horizontal directions on account of altitude were applied, as they are too small in comparison with the angular corrections required by the net adjustment to be considered. In latitude 39° the correction to a direction for height of station sighted becomes o"'ooo 066 sin 2 c^./i, hence the maxinunn correction would still be le.ss than o""o8, whereas the net adjustment in this region in several instances calls for angular corrections exceeding i". The results of the triangle side computations between the Kent Island and the Atlanta base lines, published in Coa,st and Geodetic Survey Report for 1878, pages 94-1 12, are now superseded. A portion of this work was readjusted in reditcing the tran.sconti- nental triangulation and the results are reproduced in this publication. J 6o THE EASTERN OBLIQUE ARC. Adsfraiis of rcsii/tiia;- horizontal directions, observed and adjusted, at tlie stations foDuing the'Jbase net, i844-i8gj. Kent Island South Base, Queen Anne County, Maryland. May 30 to June 4, 1S47. 30"" repeating theodolite No. u. E. Blunt, ob.server. (Observations in 1.S44 by J. Ferguson superseded by above. ) Number of directions. Object observed. Resulting direc- tions from sta- tion adjustment. Corrections from base net adjust- ment. Final seconds / // // // I Marriott 00 00 '00 + 0-03 00-03 2 Taylor 5S 53 46 -24 +o'o6 46-30 3 Kent Island North Base III 41 tS -25 — '09 iS-i6 Probable error of a single oVjservation of a direction ( 6 D. and 6 R. •69. Kent /stand North Base, Queen Anne Count}', Maryland. May 21 to 28, 1847. 30*^'" repeating theodolite No. 11. E. Blunt, observer. (Observations in i844-'45 by J. Fergu.son superseded by- above. ) 4 Kent Island vSouth Base 00 00 -oo +0-19 00-19 5 Marriott 50 05 "5 -36 -0-47 04 -89. 6 Taylor 88 35 36 '91 —0 -12 36-79 7 Linstid 121 02 04 -33 +0-16 04-49 S Swan Point iSi 09 45 '47 +0-24 45 -71 Probable error of a single observation of a direction (6/?. and 6 y?. ) , Ci = ±0" -68. Swan Point, Kent County, Maryland. October 16 to 21, 1848. 30^'" repeating theodolite No. E. Blunt, ob.server. ( Oliservations in 1845 by J. Ferg / uson superseded by above. ) // // 00 -00 —0 -23 // 34 Kent Island North Base 00 59-77 35 Einstid 56 oS 57 '92 +0-52 58-44 36 Pooles Island 169 16 25 "5' —0-29 25-22 Probable error of a single observation of a direction (6 D . and 6 A'. ) , e^ - = ±1" ■35- Taytor Anne Arundel County, Maryland. June 8 to i( 5, 1S47. jQCra repeating theodolite No. E. Blunt, observer. (Observations in 1844 by J. P'erg uson superseded by above. ) / // // // 10 Kent Island North Base 00 00-00 + 0-36 00-36 II Kent Island South Base 38 36 52-37 -0-23 52-14 12 Marriott "9 32 44-32 +0-53 44 -85 9 Linstid 247 12 54-29 -0-66 53 -63 Probable error of a single observation of a direction ( 6 D. and 6 R.), e,= ±0" 66. Pooles /stand, Harford County, Maryland. May 17 to 27, 184S. 30- ' repeating theodolite No. E. Blunt, observer. (Observations in 1845 by J. F'erg uson superseded by abov e.) / // // // 31 Swan Point 00 00 -00 +0-30 00 -30 32 Linstid 36 22 15 '13 +0-I7 15-30 33 Finlay 116 06 Osbonies Ruin 170 34 Turkey Point 225 05 54-92 06-56 01 -56 -0-47 54-45 Probable error of a single observation of a direction (6 D. and 6 A'. ), t'l = iho'^-69. BASE LINES AND BASE NETS. 6l Abstracts of rcsnttiiii^ /lorirjoiila! directions, observed and adjusted, at the stations foniiini; the Imse net, /8.pf-/8g7 — continued. Webb, Anne Arundel County, Maryland. July lo to August 14, 1848. 60 "' direction theodolite No. 2. A. D. Bache, observer. October 21 to December 2, 1850. 75 "' direction theodolite No. I. A. D. Bache, observer. September 18 to 25, 1868. 75^^'" direction theodolite No. i. CO. Boutelle, observer. Number of directions. Object observed. 26 Ivinstid 27 Marriott Hill Soper Stabler Azimuth Mark 25 Finlay Resulting direc- tions from sta- tion ;idjustnient. Corrections from base net adjust- ment. Final .seconds / '/ // //■ fXJ 00 -oo — n 02 59 -g^ 76 16 06 19 + 025 06 44 129 26 S'^i -53 "OO* 5«-53 178 32 04 72 'CO* 0472 1 86 55 II -56 —0 02 * I' '54 275 40 01 -37 2S9 44 43 'oi -0-23 42 78 Probable error of a single observation of a direction (D. and 7?. ), r, Number of positions of circle in 1848, XXXIII; in 1850 and 1868, V. ■94- Marriott, Anne Arundel County, Maryland, theodolite No. 11. E. Blunt, observer. No. 2. A. D. Bache, observer. November 18 to December 9, 1846. 30"' repeating May 18 to June 18, 1S49. 60"^'" direction theodolite o 00 00 'OO 32 06 10 '36 70 oS 37 "17 82 23 48 -68 107 33 48 -30 125 56 32-84 147 53 16 -80 166 06 54 '12 Probable error of a single observation of a direction (6 D. and 6 R.) in 1S46, d =zti o"'67 and of a direction (D. and R.) in 1849, <^i =± i"'io. Number of positions of circle, XI. Linstid, Anne Aritndel County, Maryland. May 24 to June 26, 184S. 60"" direction theodolite No. 2. A. D. Bache, observer. January 8 to 31, 1S97. 30'^"' repeating theodolite No. 16. F. \V. Perkins and W. B. Fairfield, observers. Telescope elevated above ground 27 '89 meters. (Ob.servations in 1844-45 by J. Ferguson sttpenseded by above.) Hill Soper 13 Webb Azinmth Mark 14 Linstid 15 Taylor 16 Kent Island North Base 17 Kent Island South Base — 029* 59 "71 +0-38* 1074 —0-24 36 93 +0-34 48-64 — '20 32-64 — '10 16-70 +0-19 54-31 +0 -70 — o-iS —0-52 — o -26 +0-75 —0-50 -fo 02 Probable error of a .single observation of a direction \^D. and A\) in 1S4S, j-, = a direction (6 D. and 6 R. ) in 1S97, <■, = ±o''''-73. Number of positions of circle, XVII. iS Finlay 19 Pooles Island Clough 20 Swan Point Hope 21 Kent Island North Base 22 Taylor 23 Marriott 24 Webb 00 00 -QO 46 42 57 -73 69 13 07 -73 77 13 16-97 102 07 23 -lo 140 56 37 -6o 175 43 02 -43 209 40 1 1 -28 275 5S 53 -59 00 -70 57 •55 16 -45 37 ■34 03 iS 10 •7S 53 61 "12 and of * From adjustment of Kent Ishuid extension. 62 THE EASTERN OBLIQUE ARC. Abstracts of rcsultim:: horizontal directions, observed and adjusted, at the stations forming the base net, 1844-iSgj — continued. Fin lay, Baltimore Count}-, Maryland. August 29 to September 11, 1844. 60"" direction theodolite No. 2. J. Ferguson, observer. October 15 to December 27, 1896. 30'^"' repeating theodolite No. 16. G. A. Fairfield, observer. Telescope above ground i'5 meters. Number of directions. object ob.served Osbornes Ruin Still Pond 28 Pooles Island C lough 29 Linstid ,lO Webb Resulting direc- tions from sta- tion adjustment. Corrections from base net adjust- ment. Final seconds. / CO '00 34-15 20-93 o 00 30 48 48 03 55 23 ID I 36 01 -26 127 19 37 -46 Probable error of a single ob,servation of a direction [D. and J\. ) in 1844, t', =± i"'52 and of a direction (6 D. and 6 R. ) in 1S96, c, =zto"-65. Number ?';'] _ j^ o"-6i where ti = number of conditions. * n Mean error of an auj^^le in ,c = in, ^/^ = ± o" -87 and probable error of the same ±: (/' -59. EXTENSION OF THE KENT ISLAND BASE NET TO THE NORTHWARD. Abstracts of rcsitltiiii;- hoi izontal directions, observed and adjusted at stations to tlic north of the net. Osbornes Ruin, Harford Count)-, Maryland. September 23 to October 2, 1844. 60"" direction theod- olite No. 2. J. Ferguson, observer. August 17 to September 20, 1896. 30*^'" repeating; theod- olite No. 16. G. A. Fairfield, observer. Telescope 14-17 meters above ground in 1S96. O / // // // Turkey Point o 00 00-00 +0-11 00 'ii Pooles Island 81 27 17-53 — o '06 1747 Finlay 158 56 33 29 —0-09 33 20 Principio 324 49 48 33 Probable error of a single observation of a direction (/'>. and R.) in 1S44, t', == i"'33 and of a direction (6 D. and 6 R.) in 1896, <■, =4ro"-35. Number of positions of circle in 1844, VI. Turlzcy Point, Cecil County, Mar3-land. May 31 to June 17, 1S45. 60*^'" direction theodolite No. 2. J. Ferguson, observer. September 30 to October 19, 1896. 35"" direction theodolite No. 10. J. Nelson, observer. Telescope 2-08 meters above ground in 1896. o / // // // Pooles Island Osbornes Ruin Principio Probable error of a single observation of a direction i^/^. and A'.) in 1S45, <•, =2= i"-49 and of a direction in 1896, c, =rto"-62. Number of positions of circle in 1845, VI; and in 1896, XII. 00 00 "OO +065 0065 44 01 48 -72 —0-44 4S-2S 131 14 41 -24 .... 64 THE EASTERN OBLIQUE ARC. Abstracts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the zuesliuard and southward. Hill, Prince George Count}', Maryland. June i8 to July 15, 1S46. 60-"' direction theodolite No. 2. A. D. Bache, observer. August 8 to October 4, 1850. 75-'" direction theodolite No. r. A. D. Bache and A. A. Humphrey.?, ob,servers. October 9 to November 12, 186S. 75'^^'" direction theodolite. No. i. CO. Boutelle, observer. Telescope 1676 meters above ground in 1868. Do. .It fi „„i i^orrecnon irom ,.• , Objects observed. ReM.ltsofloc.il figure adjust ^••"■' •' aojiistment. *= „,<>„t seconds -f '10 42-57 + '20 57 70 -0-31 40 -40 Peach Grove o 00 00 'oo — o '30 59 70 Causten 5 54 28 '96 "Sugar Loaf 37 48 42-47 Stabler 65 16 57 '50 Soper 69 14 4071 Azinuith Mark 125 08 23 "97 Webb 125 oS 24-12 +0-I2 24-24 Marriott iSi 48 56-12 +0-20 56-32 Probable error of a single observation of a direction (/•'.and /\'.),et= =ho''-90. Number of positions of circle in 1846 and 1850, V: in 1S68, VII. Soper, Montgomery County, Maryland. June 19 to July 23, 1850. 75*^"' direction theodolite No. i. A. D. Bache, observer. o / // /, // Webb o 00 00 -00 — o '08 :Marriott 39 41 37 '08 — 0-17 Hill 75 01 10-92 +0-24 .Azimuth Mark Cau.sten Stabler 233 17 .... 09-98 Probable error of a single ob.servation of a direction ( /). and A'. ),<;',= zto^'-gi. Number of positions of circle, V. Stabler, Montgomery County, Maryland. July 17 to Septeml)er 3, 1869. 75'"' direction theodolite No. I. C. O. Boutelle, observer. Instrument 16-76 meters above ground. Hill Peach Grove Bull Run Maryland Heights Sugar Loaf Webb Soper Probable error of a single observation of a direction (D. and A'. ),e,— ±: I'^'oS. Number of positions of circle, VII. 00 00 -00 39 41 37 -08 75 01 10-92 89 30 15 -co 122 09 57 '30 23,3 17 59 •92 36 -91 II -16 00 00 -QO —0 -24 59 '76 63 40 03 -06 -0-37 02 -69 87 1 1 16-57 +0-04 16 -61 131 27 54-59 +0-06 54 -65 134 09 42-34 +0-48 42-82 297 19 37 -68 +0-01 37 -69 342 13 41 -17 -00 41 -17 CofiHt (in(L Geodetic Survey, 1901. The Eastern ObHtjue. Arc. No. 10 WfeiA Md.ry/and HeigJits Suxfor Loaf Ml Ma rah (til Fork Kpfit In hind \ Marriott THE KENT ISLAND BASE Triangulatioii (o the Westward and Soiithwaid Staiiiio Milfs l^nhttrco h'i>n' o 10 2" .10 'lO ^0 Kilometers lo (1 10 ;;o :o HC !W«HISKrt BASE LINES AND BASK NETS. 65 Ahstrads of resulting horizon /a/ directions observed and adjusted at stations forming the extension of the Kent Island base net to the westward and southward — coutinuerl. Peach Grove, Fairfax County, Virj^inia. October 11 to November ,= ± o" -60. Number of positions of circle, XI. Mount Marshall, Rappahannock County, Virginia. July 18 to September 7, 1S74. 35'^"' direction theodolite No. 10. A. T. Mosman, observer. a / // // // F'ork Maryland Heights 1S4 15 4956 —0-26 Sugar Loaf 202 41 37 50 +0-36 Bull Run 225 17 06-78 +0-19 Peach Grove 229 31 2999 — o -28 Clark Peters Probable error of a single observation of a direction {^D. and R. ),<•,= d= i" -29. Number of positions of circle, XI. 4192 — No. 7 — 02 5 00 00 -00 45 27 1579 + 0-72 I6-5I 65 36 50 -72 —0 -II 50-61 120 27 54 '38 +0 -10 54 -48 306 43 36-06 —0 -46 35-60 325 05 39 25 352 26 27 -18 —0-26 26 -92 00 00 -00 1 84 15 49-56 202 41 37 -50 225 17 06 -78 229 3^ 29-99 3" 50 33-98 336 20 36-44 49 -30 37 -86 06 -97 29 •71 66 THE EASTERN OBLIQUE ARC. Ahstiacts of resulting horizontal directions observed and adjusted at stations forming the extension of the Kent Island base net to the ivestxoard and south-ward — continued. Bull Run, Fauquier County, Virginia. September 22 to November 2S, 1S71. 75' '" direction theodolite No. I. CO. Boutelle, observer. objects observed. Kcsults of local adjustment. Correction from ,,. , fi-ure adjust- ^"''\' n.eut seconds. Azimuth Mark Clark Fork Mount Marshall Maryland Heights Sugar Loaf Stabler Peach Grove 00 00 '00 1 07 09 -35 33 03 17 -5! 53 39 05 -53 157 20 07 -ts 190 54 06 -98 225 12 03-95 242 29 57 -85 Probable error of a single observation of a direction ( D . and A^. ) , 6'i : of circle, VII. +0-II 05-64 +0 -49 07 '64 — o "68 06 '30 +0 'oS 04 '03 o -00 57 -85 1^09. Number of positions Maryland Heights. Washington County, Maryland. September 16 to October 28, 1870. 75"" direc- tion theodolite No. i. CO. Boutelle, observer. vSugar Loaf 00 00 -QO — Q-lS 59-82 Azimuth Mark 57 03 '66 Stabler 3 33 53 '32 -0-24 53 -08 Peach Grove 30 31 14-53 +0-84 15-37 Bull Run 71 ^5 27 -26 -0-50 26-76 Mount :Marshall 106 43 12 '67 -(-0 -08 '2-75 Probable error of a single observation of a direction ( D. and R. ),6-x = ±0'' ■93- Number of positions of circle, VII. Clark, Orange County, Virginia. July 24 to September 5, 187 1. C O. Boutelle, observer. 75"'" direction theodolite No. i. Spear Peters Humpback Azimut'h Mark P'ork Mount Marshall Bull Run Probable error of a single observation of a direction ( D. and R. ) , t'l = ± i -03. of circle, VII. 00 00 -00 II 21 47 -QO 24 09 37 ■37 55 29 20 -96 7« 26 10 -17 122 25 05 -12 163 19 47 57 -I '35 +0-97 +0 -02 +0-4S Number of positions 59 -88 36 •02 II ■t4 05 •14 48 05 basp: links and bask nets. 67 Abslracls o/rcsullinir horizontal dircclions observed and adjusted at stations formiiif; the extension of the Kent Island Imse net to the roestiuard and southiuard — continued. Fork, Madison County, Virginia. ()ctot)cr 12 to December 24, iserveS 36-93 +0-29 37-22 0-47 4 -443 721 ' 27 779 29 Soper 39 41 37 -08 - - -09 36-99 049 4 392 324 7 24 678 -84 Webb 102 15 58-28 -00 58 -28 -48 4 -577 012 I 37 75S -27 Marriott 3^ 02 26-57 -0-38 26-19 0-49 4 376 775 6 23 810-89 Soper 75 01 10 -92 +0-32 II -24 -43 4 -443 721 I 27 779 -29 Webb 49 05 06-19 -ot) 06 - 1 9 -42 4 -337 076 1 21 730 -82 Hill 55 53 43-41 +0 -43 43 •S4 0-42 4 -376 775 S 23 810 -90 Soper 35 19 33 -84 -t-0-41 34-25 -40 4 -373 719 9 23 643 "94 Marriott 32 06 10-36 +0-67 II -03 40 4 -337 076 2 21 730 -82 Hill 112 34 15 -41 f -5 1 15 92 -40 4 -577 012 2 37 758 -28 Stabler 44 54 03-49 -o-or 03 -48 -oS 4 -376 775 7 25 810-90 Webb 8 23 06-84 — -02 06-82 o"oS 3 -691 882 4 4 919 06 Soper 126 42 49-94 -oS 4-432 017 4 27 040 -67 JO THE EASTERN OBLIQUE ARC. No. 23 24 25 26 27 2S 29 30 31 32 IVcUvu and southern extension uf Kent Island t>ase net- -continued. stations. Observed angles. Correc- tion. .Spher- ical angles. Spher- ical excess. Log. dis- tances. Distances in meters. / rr // // // Stabler 62 40 22-32 ~o -26 22 -06 0-53 4 -443 721 I 27 779 -29 Webb 57 28 13 '03 —0 -02 13-01 0-54 4-420 998 3 26 363 -21 Hill 59 51 26-62 -0-08 26 -54 0-54 4 -432 017 4 27 040-67 Stabler 17 46 18 -83 -0 -245 18 -585 -034 4 -337 076 1 21 730 -82 Soper 15S 15 58 -820 0-033 4-420 998 3 26 363 -21 Hill 3 57 43 '21 -0-514 42 -696 -034 3 -691 882 5 4 919 -06 Peach Grove 51 03 01 'OO —0-08 00 -92 '62 4 -420 998 3 26 363-21 Stabler 63 40 03 -06 -0-13 02-93 -62 4-482 609 8 30 381 -54 Hill 65 16 57 '50 +0-50 58-00 -61 4 -488 456 8 30 793 -34 Sugar Loaf 18 22 03-65 -62 4 -420 99S 3 26 363-21 Stabler 134 09 42 '34 + 0-73 43-07 -61 4-778 281 4 60 017 -99 Hill 27 28 15-03 +0 -10 15-13 -62 4-586 513 6 38 593 '45 vSugar Loaf 45 42 51 -12 + -20 51 -32 0-95 4 -488 456 8 30 793 '34 Stabler 70 29 39 -28 + 0-85 40-13 -94 4-607 957 7 40 546-91 Peach Grove 63 47 31 -09 +0-30 31 -39 -95 4 -586 513 6 38 593 -45 Sugar Loaf 27 20 47-66 -95 4 -482 609 8 30 381 -54 Hill 37 48 42 '47 ^-o -40 42-87 0-95 4-607 957 8 40 546 -92 Peach Grove 114 50 32 -09 -)-o -22 32-31 0-94 4-778 281 4 60 017-99 Maryland Heights 3 33 53-32 -0 -059 53 -261 -104 4-586 513 6 38 593 -45 Sugar Loaf 173 44 18 -32 +0 -562 18 -882 -104 4-830 573 67 697 -56 Stabler 2 41 47-75 +0-419 48 -169 -104 4-465 432 7 29 203 -35 Marylanil Heights 30 31 14-53 +1 -02 15 -55 0-79 4-607 957 7 40 546 -91 Sugar Loaf 128 01 27 -20 +0-36 27 -56 0-79 4 -798 611 62 894 -26 Peach Grove 21 27 18 -70 +0 -.56 19 -26 0-79 4-465 432 7 29 203 -35 Maryland Heights 26 57 21 -21 + 1 -08 22 -29 1-63 4 -488 456 8 30 793 -34 Stabler 67 47 51 -53 +0-43 51 -96 '-63 4-798 611 I 62 S94 -28 Peach Grove 85 14 49 79 +0-86 50-65 I -64 4-830 573 67 697 -56 Bull Run 33 33 59 -83 -1 -16 58-67 I -20 4-465 432 7 29 203 -35 Maryland Heights 71 25 27 -26 -0-31 26-95 I -20 4-699 551 7 50 067 -01 Sugar Loaf 75 00 38 -59 —0-62 37 -97 I -19 4 707 753 2 51 021 -49 Bull Run 67 51, 56-80 —0 -40 56-40 2 -70 4-830 573 67 697 -56 Maryland Heights 67 51 33-94 —0 -26 33-68 2-71 4-830 553 5 67 694 -52 vStabler 44 16 38 -02 f -02 38-04 2-71 4-707 753 2 51 021 -49 Hull Run 85 09 50 -70 —0-49 50 -21 1 -77 4 -798 611 62 894 -26 Maryland Heights 40 54 12-73 -I -33 11 -40 .-78 4 -616 253 41 328 -82 Peach Grove 53 56 04-40 -0 -68 03-72 1-78 4-707 753 3 51 021-51 Bull Run 34 17 56-97 +0-76 57 '73 I -62 4-586 513 6 38 593 -45 Sugar Loaf 98 43 39-73 + 1 -iS 40-91 I -61 4-830 553 5 67 694 -52 Stabler 46 58 25-77 +Q-44 26-21 1 -62 4-699 55' 6 50 067 -00 BASE LINES AND BASE NETS. 71 33 34 35 36 37 3« 39 40 41 42 43 44 45 IVcshTll and son/Zicrii c.vlfi/sutii of Kcnl Island base net — -continued. Stations. ( )bservc(l aiij^les. Correc- tion. Spher- ical angles. Spher- ical excess. I,og. dis- tances. Distances in meters. / // // // // Hull Run 51 35 50-87 4-0-68 51 -55 1 -37 4 (*'>1 957 7 4" .546 -91 Sugar Loaf 53 00 48 -61 io-98 49 "59 '-37 4-616 253 41 328 -82 Peach Grove 75 23 23 'lo ^a-i2 22-98 ■-38 4-699 551 7 50 067 01 Bull Run '7 >7 53 '90 -08 53 •«2 f) -70 4 -488 456 8 30 793 -34 vStabler 23 31 13-51 +0-41 13-92 -70 4 -616 253 I 4J 328 -83 Peach Grove 139 10 54 '9 1 o-i8 54 -37 0-71 4 -830 553 6 67 694 -53 Mount Marshall iS 25 47-94 +0-62 4S -56 ,79 4-465 432 7 29 203 35 Maryland Heights 106 43 12 -67 + 0-26 12-93 1-78 4-946 793 1 88 469 -4 1 Sugar Loaf 54 51 03-66 -|-0 -21 03 -87 I '79 4-878 122 3 75 530 -49 Mount Marshall 41 01 17 -22 + " -45 17 -67 I -88 4-707 753 2 51 021 49 Maryland Heights 35 17 45 -41 + 0-57 45 •9-'^ I -88 4 652 400 4 44 915-93 Bull Run i«3 41 01 -62 +0 •3 88 469 41 Mount Marshall 4 14 23-21 - -46S 22 -742 -242 4 616 253 41 328 -82 Bull Run 171 09 07-68 ( -III 07 -791 -241 4 -934 439 85 988-24 Peach Grove 4 36 29 -66 ■\ -532 30-192 -242 4-652 400 4 44 9>5 93 Clark 40 54 42 -45 +0-46 42-91 2 -07 4 652 4fxi 4 44 9 '5 93 Mount Marshall 86 33 27 -01 -25 26 76 2 06 4-S35 447 I 68 461 61 Bull Run 52 3' 56-29 "t-o -24 56 -53 2 -07 4 -735 883 3 54 435 -63 Fork 24 4" 24 -02 ~i-lo 22 62 I -02 4-652 400 4 44 915 93 Mount Marshall 134 42 53 -03 —0 19 52-84 I -03 4-883 177 2 76 414-75 Hull Run 20 35 4S-13 -0 -52 47-61 I 02 4 -577 810 2 37 827 -72 Fork S7 51 45 -06 ~I -25 43 -81 I -29 4-735 883 3 54 435 -63 Mount Marshall , 4.S (19 26-02 +0-05 26 07 1 -30 4 -608 327 40 58 1 40 Clark 43 S'"^ 54 95 0-94 54 -01 ' -30 4 '577 8 10 3 37 827 -73 I-'ork 63 U) 2 1 04 : 0-15 21 -19 2 34 4 -835 447 1 68 461 61 Bull Run 3' 56 08-16 1 076 08 -92 2-34 4-608 326 9 40 581 -39 Clark S4 53 37 -40 -0 -48 36 -92 2 '35 4-883 177 2 76 414-75 Humpback 27 01 48 -28 t I -04 49 -32 2 46 4-608 326 9 40 581 -39 I'ork qS 41 42 -28 -\ -67 42 -95 2 47 4-945 819 I SS 271 -22 Clark 54 16 32 -80 i 2 -32 35-12 2 46 4 -860 307 4 72 404 -8q 72 THE EASTERN OBLIQUE ARC. IVt'stei-i! No. 46 47 48 49 Spear Humpback Fork Spear Humpback Clark Spear Fork Clark Tobacco Row Humpback Spear son/ //(V7/ twiensioi! of Kent Island ha St )iet~ -contiuued. Observed angles. Correc- tion. .Spher- ical angles. Spher- ical excess. Log. dis. tances. Distances in meters. / // // // // 32 oS II -61 +0-49 12-10 2 '3 4 -S60 307 4 72 494-89 128 45 52-84 +0 -I I 52-95 2 -14 5-026 395 5 106 266 -29 19 06 01 '45 —0 -lo oi -35 2 •13 4-649 283 4 44 594-7' 54 06 29-41 +0 -61 30-02 3 •26 4-945 819 1 88 271 -22 lOI 44 04-56 -0 -93 03 -63 3 ■27 5 -028 099 9 106 6S4 -15 24 09 37 '37 -I -23 36-14 3 -26 4-649 283 4 44 594-71 21 58 17 -80 +0-12 17-92 3 •59 4 -608 326 9 40 581 -39 79 35 40-83 +0-77 41 -60 3 ■59 5 -028 100 106 684 -17 78 26 10-17 + 1 -08 II -25 3 •59 5-026 395 5 106 266 -29 59 27 05 -42 — I '08 04 '34 I ■37 4-649 283 4 44 594-71 46 51 42-66 -I '3' 41 '35 I •37 4-577 326 2 37 785 -59 73 41 19 -qS — 0-66 18-42 I ■37 4-696 339 5 49 69S -07 Determination of the probable error of the lengtli of the sides Osbomes Rjiin to Turl<:ev Point, and Tobaeeo Row to Spear. In connection with the Kent Island base net the probable error of the side Linstid to Finlay was rigorouslj- computed, and was found to be ±0-33 meters; which equals ToT^fiTTu part of the length of the side. There are three triangles between this side and the side O.sbornes Ruin to Turkey Point; but, instead of computing the additional prob- able error arising from their measure separately, it will suffice, when estimating the probable error of the chain of triangles between the Fire Island and Kent Lsland bases to include the.se three triangles as part of the chain; otherwise, the probable error of the line ma\- be taken as about yoo^-oirTr part of the length. For the extension southward the probable error of the side Webb to Marriott was rigorously computed and found to equal ±0-22 meters, which is about tt2'-2tto part of the length. For that part of the triangulation lying between Webb to Marriott and Fork to Clark the probable error was found to be foa'Triyiv part of the length, and the .same fraction may be used for the extension thence to the line Tobacco Row to vSpear. Descriptions of the base-net station.s- are given in the account of the Transconti- nental Triangulation, etc.. Special Publication No. 4, Washington, 1900. 5. THE ATLANTA BASE AND BA.SE NET, GEORGIA, 1872-73. Location, measurement, and resnltini; lenoth of the Atlanta base line, i8'j2-'j^. The Atlanta ba.se is located on Peach Tree Ridge, Georgia, about 24 kilometers (or 15 .statute miles) northeast of the city of Atlanta. It is the .seventh and last base measured with the Bache-Wiirdeniann apparatus, and is the only one measured with it more than once. It is 9)^ kilometers (or 5-81 statute miles) in length and was meas- ured three times. There is a very full description of the operations in Coast Survey Report for 1873, Appendix No. 12, pages 123-131, and the description of the apparatus BASE LINES AND BASE NETS. 73 is given in Coast Survey Report f(;r 1854, Appendix No. 35, and in Coast Survey Report for 1873, Appendix No. 12. F^urther remarks will be found in the account of the Dauphin Island and the Hpping bases in this publication. It will also appear from the seven values collected on page 131 of the Rejjcjrt tor [873 that the average accuracy reached with this apparatus is about goo'ouu P^rt of the length measured. In \-iew of the complete publication already made, it will .suflfice to give the present account in an abbreviated form. The middle point of the.base is in latitude 33° 54'"4 and longitude 84° i6'-5, with a mean azimuth 52° o8''2. The measurements were made by Assistant C. O. Boutelle. The first and second measures were made in opposite directions in Novemljer and December, 1872, and in January, 1873, and the third was made in July and August, 1873. The three measures were accomplished in 17, 13, and 14 working days, re.spec- tively. In connection with these several measures the tubes* were frequenth' compared for length with the standard bar, which was immersed in glycerin during the July and September comparisons. The summit of the ridge is narrow and crooked, Imt the slope of the measurement was confined within the maximum inclination the tubes would bear, namely, 5°. A gulch near the southwest end was crossed on trestlework consisting of two separate structures. The approximate elevation above sea level is 320 meters. The terminals are marked by granite monuments and the subdi\-isionsof the line by small granite posts. The length of the 6-meter standard bar is 5'" '999 941 at 0° C.,and its coefficient of dz 2 expansion o '000 01 1 54. The luimerous comparisons made for standardization of the ±4 tubes and for testing their compen.sation showed that the latter was .still clo.se: that is. about 2 1 parts of 22 remained compensated between the range of temperature 0° to 22° C. , but between the temperatures from 22° to 38° C. the tubes compen.sated only aliout 10 parts in 11. The comparisons were made with the Saxton reflecting comparator Xo. i . for which we have for the period November, 1872, to January, 1873, one division at 4>2° C. equal i'384 microns and at 19° C. r378 microns, values answering for the case ±3 ±3 of the first and .second base mea.sures In connection with the third measure, ob.serva- tions in July and September, 1873, gave r div. = i'376 /'. We have also i turn of the screw at the temperatures 4°, 19°, and 28° C. equal to 35o'9, 352"3. ^uid 353'o6 scale ± -18 divisions, respectively. As the result from the above comparisons we have the following values for the length of the tubes, in which the uncertainty from the length of the standard is included: For first and second nieasnres and fcr third measure Tube I, = 5'" '999 999 7 + o'ooc^ 003 37 ( / - 1 1^-2 C. ) ' =b 144 Tube 2=5 -999 647 8 ; Q-txx) 004 84 (/ — U^'2 C. ) ±193 Tube I , = 6""ooo 0S4 6 4- o-ooo 009 54 (/ — 27''-6 C. ) ±112 Tube 2=5 999 730 3 t 0XXX1 cxjS 01 (/ — 27° "S C. ) ±116 ♦Before making the compari.sons tube No. i was supplied with a new agate. The Borda .-teate or differential thermometer as applied to the tubes is shown on plate No. iS in the Coast Sur\-ey Report for 1S7,;. 74 THE EASTERN OBLIQUE ARC. The minimum temperature at which the tubes were used was — 7° 7 C, and many were laid with temperatures below the freezing point; the maximum temperature at which the tubes were used was 41 '^'7 C, and many were laid with temperatures above 38° C. The three thermometers attached to each tube were read and the mean values were corrected for graduation errors. The maximum inclination of a tube laid was 4° '7, and there were a great many with inclinations of 4°. The ruggedness of the ground caused the sum of the inclination corrections for the whole base to mount up to io""22i2 in the first and to 10'" '0375 in the last measure. Fractional parts of a tube at the base monuments and intermediate marks were measured with the brass Lenoir meter of the vSurvey, which is of standard length at 13° '6 C. The following table shows the temperature of the tubes during the measures of the several parts of the base, their lengths as measured, corrected for inclination, but not reduced to sea level, and exhibits the difference of the individual measures from the mean of the three measures: Subdivisions of base. Temperatures, Resulting length. Mean. Discrepancies. First measure. Second mea.sure. Third measure. First Second, measure. measure. Third measure. First measure. Second measure. Third measure. SW to I I to n U to M .M to IV IV to V V to NE c. i5'i3 5-10 6-84 II "06 14-0? 11 31 C. 5-62 9 "44 4 -28 2-97 5 "57 12 92 C. 34-33 . 33 "94 32 '56 32 03 31-96 30 "74 I 635 "974 9 I 642-313 6 I 234 -383 3 I 348 -886 2 I 785 -709 I 691 -692 I 635 -96S I 642-3173 I 234 -388 I 348 -880 6 1 785 -704 8 I 691 -692 5 I 635 -966 4 I 642-3125 I 234-391 8 1 348 -8S5 I I 785 -705 2 I 691 -681 5 I 635 -969 8 1 642 -314 4 I 234 -387 7 I 348 -884 I 785 -706 3 I 691 -688 7 Ill III . -5-1 +0-8 +4-4 — 2-2 -2-7 -3-3 mm. + 1-8 -2-9 -0-3 +3-4 + 1-5 -3-8 mm. +3-4 + 1-9 -4-1 -I -J + 1 -I 4-7-2 Whole base 10-58 6 -.So 32-59 9 338 -959 9338-951 2 9 338 -942 .'s 9 338 -950 9 The frequent changes of sign in the above discrepancies may be taken as a favor- able indication that the lengths of the tubes were correctly determined. In order to o]:)tain the data required to reduce each part of the base to sea level, two lines of spirit levels were carried over it, double zenith distances of Stone Mountain were measured for difference of height at Southwest Base, Middle Base, and Northeast Base, and reciprocal ob.servations were made at Stone Mountain. A line of spirit levels was carried from Stone Mountain, in 1873-74, to Augusta, Georgia; between this place and Port Royal the railroad levels were utilized, and the elevations refer to Atlantic half tide at Beaufort, vSouth Carolina. The resulting height of vStone Mountain is 5 13'" '95, and allowing i""52 for the elevation of tlie tubes above the ground, the average eleva- tion of the tubes above the half-tide level becomes 321'" '5, and the reduction of the base Whence we get for the length of the ba.se the values to sea level — = P o 4710. 9 338" -4880 4802 \ mean 9 338 479 9 meters. 47 ' 5 I Combining the mcmi of the two winter measures with the value of the summer measure, we get 9 338 "477 8 meters. We have also the distance Southwest Ba.se to Middle Base 4 5i2'"-447, and from Middle Ba.se to Northwest Ba.se 4 826-032 meters. The liorizontal angles mea.sured at these three ba.se stations and at Stone Mountain BAS?: LINES AND HASE NETS. 75 afford a check on the measure. vStartin^ with the first or sh(;rter distance and usinj^ the adjusted anj^ular measures, the length of tlie base thus trigtjnometrically deduced comes out 9 338"''502, or 22 ' in excess of the direct hnear measure. For the ])robable error of the measure of the l)a.se we have the following data: Probable error from uncertainty in length of tubes in i 556 tubes, i 556 X i^oj-i^ ±o"''02i 78. For mere measuring error we have, after forming the values ^ S-, 2: 6 '-, 2 (J^^, etc., where the f^'s are taken from the preceding tal)le of differences from the mean of three measures, assumed of equal weight, the probable error of the ba.se from the.se measures = zh o'674 ( - ' = ^ )^" where Ji — i,, hence tlie V n(n-i} J result = dco"''oo3 85, which includes errors ari.sing from defective compensation, errors of contact, of tran.sfer to ground or to monuments, of alignment and inclination, etc. Supposing an uncertainty in // of i meter, the reduction to sea level changes ± i"'"'-46. Combining the values we get the probable error of the ba.se V(2r78)="+~(y85)^+ (1-46)= = db 22--2, which equals jji'iumi P^rt of the length. The resulting length of the ba.se is 9 338'477 8 meters, and its logarithm 3^970 276 09 ±222 ± I 03 Adjiistiiieiil of tht' .Allan la base net. The base is connected with the principal triangulation by a rather complex system of triangles, which made the placing of the boundary of the net to some extent an arbitrary act, except in so far as the labor involved set a limit to it. The net as it had been selected and adjusted in 1876 is here retained as sati.sfactory. The only change that could be made would be the introduction of the small corrections to the horizontal directions for height of object observed upon, which it was not customary to introduce at that time. The heights of the 10 stations involved are as follows: Appyoxiiitatc hcti^hls of slalioiis alwzY llw Atlantic Ocean. Mettrs. I'ect. Atlanta Southwest Base Atlanta Northeast Base Atlanta Middle Base Stone ^Mountain* Academy Kenesaw Sweat Mountain Sawnee Pine Log Grassy 3 1 •^•5 ■ 045 326 1 070 325 1 06S 514 1 6S6 346 1 136 55" 1 S09 516 1 694 600 I 967 7 '3 2 340 I 003 3 290 * Klevatio!! from spirit level.s. .si.V'o?. 76 THE EASTERN OBLIQUE ARC. No. 12. This reduction of the directions to sea level, a maximum in the case of line Pine Log to Grassy, is less than o"'o-j, and in general it is less than one-half of this amount. It is therefore fully covered by the observing error of the directions which on the aver- age amounts to "^ ^ or o"'i9; besides, a number of directions require corrections in the 77 figure adjustment of more than i". As shown in the diagram, the net comprises Testations which were occupied between 1872 and 1874; two observers were engaged in the work and three different instruments were employed, one being a repeating theodolite. The ad- justment of the observations of directions at a .station was made by Bessel's method, and the results are presented in the abstracts, where, for con- venience, the resulting cor- rections due to the figure or net adjustment have been add- ed. The latter computation involved 29 conditions which had to be .satisfied. Here weights to the directions were introduced, depending upon the same principle as ex- plained in the case of the ad- justment of the Epping base net. In accordance with the method of application of weights to the directions in a net adjustment, we derive the mean error of a triangle from the sum of the squares of the closing errors of the 30 triangles involved and find /91 ' I y =zti"'74; hence also the probable error of a direc- JD Grassj y^ / \ '\' ^ / / \ '- ^, // \ ^ c^_Pine Log / \ 1\ ^^/r---_ \ 1 \ / / ,-^;^ / Sa wnee 1 '^X / .^^^y^ / \ \ Sweat Mt.)!:^^ \ 1 //^C~~~~~~~~^ / \ 1 './^ V^nT^^^^^^^ \ }j^KeTiesaw \ \ ^v / ^^_^ \ AcademY Atlanta Middle Base \i^ \ I Northeast Base Atlanta Southwest Base^^^^^^^^ X\ \ / Kilometers ^^^i:^^ xs\ / 5 5 10 15 ~**^oi. Statute Miles ^ tS Stone Mt. 6 5 10 1 tion, 0*674 /gri V 180 ±o"'48. Further we have the average value of the probable error of a direction derived from the measures and given in column 4 of the ab- stracts of directions=±o"'i9, whence the .square of the triangle combination error f^''^ (o"'48)" — (o"'i9)" = o""2o nearly. This value was added as a constant to each previou.sly deduced square of the observing error; hence *" = f,"+f- and the weight of each direction,/) = — . The reciprocals of these values after division by o"22' for the sake of convenience are tabulated further on. BASE LINES AND BASE NETS. 11 Abstracts: of horizontal dircdions at stations fonnin^ t/ic .Itlunta luise net, /87^-/874. Atlanta A/iddtr /;asc* De Kalb County, Georgia. January ii to 30, 1873. C. O. Uoiilc-lle, obser\-er. 75"" direction theodolite No. i. Circle used in VII positions. Resulting direc- .■\pproximate Correction Final objfc'ls ohservtd. tions from .station jirobaWe from figure seconds adjustment. error. adjustment. Number of directions. Atlanta Northeast Base Stone Mountain Atlanta Southwest Base o 00 00 '000 So 14 23 -381 I So 00 00 '037 // rO '12 o '14 o -12 - o -078 -0193 01 15 59 922 23 '574 59^922 Mean correction o '000 Probable error of a single observation of a direction (/J. and /v*. j, ('2 = d=o"'75. Atlanta Sout/iivcsi Basr, De Kalb County, Georgia. Fetiruary 10 to 22, 1S73. C. O. Boutelle, observer. Instrument as before. Circle u.sed in VII positions. 5 Kene.saw 00 00 -000 ±015 —0 -026 00 026 6 Sweat Mountain 34 24 39 '322 14 -0130 39 192 4 Atlanta Middle Base and North- east Base 118 38 10 '842 -12 -0-114 10 -728 7 Stone Mountain 184 22 33 "046 -II ^0-219 33 265 Atlanta, City Hall spire 271 16 31 "46 Atlanta, Capitol flagstaff 273 14 57 -oS Mean correction o "ooo Probable error of a single ob.servation of a direction {D. and A'. ), c, = ±o"'68. Atlanta Northeast Base, Gwinnett County, Georgia. February 27 to March 21, 1S73. Observer and instrument as before. Circle used in VII positions. 12 Stone Mountain 8 Atlanta Middle Base and South- west Base 9 Kenesaw 10 Sweat Mountain II Sawnee 13 Academy ±015 -o ■082 O 00 00 "000 82 49 01 -328 129 23 28-311 ■56 57 34 '651 222 15 52 -S40 293 13 58-560 Mean correction o -000 Probable error of a single observation of a direction {P. and R.^, i\ = zto'^-go. 00 -0S2 13 ^0371 01 -699 14 -0-904 29-215 15 -i-o 070 34721 '7 — o-6oi 52 239 16 0-826 57 734 *This station was occupied eccentrically oni-0423 off the line connecting Northeast Base and Southwest Base and the above directions are reduced to the line. 78 THE EASTERN OBLIQUE ARC. yihs/racts of horizontal dimiioNS at stations foriiiinff the Atlanta base net, /Syj-/S/./ — continued. A'r/wsaic. Coblj County, Georgia. June 25 to July 18, 1873. F. P. Webber, observer. Instrument as before. Circle used in VII positions. Number of directions- Objects observed x6 .Sweat Mountain 17 Sawnee 15 Atlanta Northeast Base 14 Atlanta Southwest Base 18 vStone Mountain Carnes Lavender 19 Pine Log Re tioi a suiting direc- s from station djustment. Approximate probable error. Correction from figure adjustment. Final seconds. / // / f /' // 00 00 '000 ±0 "20 +0 -049 00 -049 4 36 07 -630 0'20 +0 ■! 10 07 740 50 "3 37 '342 0-28 + -226 37 -568 64 50 59-613 0-27 + -290 59 '903 66 36 1 1 -903 0-24 — I '056 ID -847 224 20 15 '036 0-36 15 '063 252 07 00 -675 0-54 00 702 303 37 21 -586 0-41 + -543 22 -129 Mean correction +0 '027 Probable error of a single observation of a direction {D. and R. ), c, = ±1" "Si. Sivcat Mountain , Cobb County, Georgia. September 10 to October 3, 1873. F. P. Webber, observer Instrument as before. Circle used in VII positions. O 00 00 "000 rto'ii -l-o'oi6 00 '016 32 34 43 "053 100 54 55 -825 145 16 24-035 186 42 56 -639 236 54 39 ■''546 257 37 42 923 266 39 06 ■ 6 1 6 279 15 3S'2'S9 Mean correction — o '036 Probable error of a single ob.servation fif a direction ( />. and R. ), i\ = ±r" '25. Stone Mountain, De Kalb County, Georgia. December ii to December 20, 1873. C. O. Boutelle, observer. 50"'" direction theodolite No. 3. Circle used in XI positions. 22 Kenesaw Carnes 26 Pine Log 25 Grassy 23 Sawnee 27 Academy 21 Atlanta Northeast Base 24 Stone Mountain 20 Atlanta Southwest Base 1 1 -|-o '016 •26 ■21 -0-273 ■18 + 0-529 21 +0 -669 •27 — I -131 ■25 -0 -835 ■19 +0-916 ■18 -0-183 55 ■552 24 ■564 57 30S 3« ■7>5 42 -oss 07 •532 38 -106 38 36 35 39 37 40 41 Spire near flagstaff Kenesaw Atlanta Southwest Base Atlanta Middle Ba.se * Sweat Mountain Atlanta Northeast Base Sawnee Academy Alcova 00 00 -QOO rbO-23 40 54 49 -578 -26 -0-375 49 '203 43 32 1 1 -836 -19 -0-245 II -591 58 02 13 -204 0-17 -0-314 1 2 -890 60 57 46 -579 0-24 +0-915 47 '494 74 58 48 -469 -10 —0 -649 47 -820 103 57 45 -410 0-14 +0 -627 46 -037 145 43 1 7 '505 -20 +0-119 17 -624 207 54 55 '333 -21 Mean correction +o-oii Probable error of a single observation of a direction {D. and R. ), 1?, = ±i''-i4. * Result reduced to Middle Base in line, reduction ^ BASK LINE.S AND HASP", NETS. 79 Ahstrach of horizontal dirccliinis at ■stations /'onin)iL; t/ir Atlanta tiasc net, /Hyj-/8j4 — continue'!. Sawiiec, Forsyth County, Gcorj^ia. (Jctobcr 7 to Novenibcr 12, 1^73. C. (J. Houtelle, obser%'er. yjcm direction theodolite No. r. November 26 to December 4, 1873. Same observer. 50'"' direc- tion theodolite No. 3. Circle used in VII and IV positions, respectively. Number uf directions. Objfcts ohscrvfd. A/.inuitli Mark Alcova 34 Academy 31 Stone Mountain 28 Atlanta Northeast Base 29 Kenesaw 30 Sweat Mountain 33 Pine Log 32 Grassy ' Blood Yonah Skitt Currahee Resulting direc- tioii.s from statioi: adjustment. O CX) CK) 'OfJO 5 59 5"'2"3 13 35 48'3«6 3« 56 35 773 52 13 32 -259 93 53 42 795 96 00 32 ■f)S6 142 50 58 -425 191 04 26-154 240 44 00 '564 263 1 1 38 -044 273 57 55 '373 286 (jg 07 '228 Approximate- probable error. zto '09 o -24 o •26 o '23 -21 "■25 O '22 0-I7 O -22 o -24 o"3i 0-32 O "22 Correction from fi;(iire adjustment. + 0-847 + 1-311 -o -274 -o -856 —0-396 -o'353 -o -244 Pinal .secoiid>. 49 153 37 -"^A 3' 985 4' ■9?,9 31 fXjft 58 -072 25 -910 Mean correction -^o -005 Ninety-two series were measured with theodolite No. r, and 40 with theodolite No. 3. Proljable error of a single observation of a direction (/?. and iV. ), r, = rbi"-34. Grassy, Pickens County, Georgia. Jul}' 13 to 31, 1874. C. O. Boutelle, observer. 50^^"' direction theodolite No. 3. Circle u.sed in XI positions. 44 Sawnee 43 Sweat Mountain 42 Kenesaw 45 Pine Log Johns Cohutta Blood Skitt o 00 00 000 43 29 35-631 51 39 33 335 41 37'o3> 59 ' 7 "050 183 15 3^^-960 261 37 28 -061 297 ;;, 10620 86 31 o -07 o -16 0-23 0-13 o -26 o-i8 0-15 o -16 +0 -228 +0 -299 — r -40S +0 755 00 •22S 35 93" 31 '927 37 784 Mean correction Probable error of a single observation of a direction {/). .uid R.),e^ = ±0" '91. So THE EASTERN OBUOUE ARC. Absfi-acts of horizontal directions, at stations fornun-o •237( 29) - o -892( 31 ) -o ■692(37)+o -311(38) I o -380(40) o= + 2 -359+0 •628(28)-o -892(31 )+o -264(34 ) + o -306(37) -o -380(40) +0 -0741 41) -0-305(50) |-o-o75(52)+o -230(53) o= — 2-792+0-403(9)— 0-500(10) +0-097(1 1 )i-o- J 76(15)^2 -439(16) -2 -616(17) +o-22o(28)-5-705(29)+5 -485(30) o=+o-463 f 0-223(23 ) -0-238(25 ) +0-016(26 ) -0-222(43 ) -^0-210(44 )+() -012(45) +0 -194(47 )-o-4o4(48)+o -210(49) o= + i -619-2 -7557(i6) + 2-6i57(i7)+o-i4oo(i9)+5 -7048(29) -5 -9022(3o)+o -1974(33) -ro-5032(46) 0-6971(47) [0-1939(48) o=+5 -491-2 •6i57(i6) + 2-6i57( 17) -o-42i2(22)+o-42i2(25)-^5-7048(29)-5 -6861 130) — o-oi87(32) + i -8885(42)-2 -I io4(43)+o -2219(44) Equations, of corrctativc's. (i) = i-o(+C,) (2) = i-o(-C,-C.) (3) = i-o(+C.) (4) = i ■o(— C3 + C5— o -095 C,5-o-ii6 C;o) (5-) = i-o( + C6-C8) (6) = i -o(-C4-C5+Cs+o-02i Co) (7) = i •o(+C3+C4-C6+o-o95 0,5+0-095 C^o) (5) = i ■o(+C= + C,-C5-o-o26 0,5-0-226 0=,+o-i4o C™) (9) = i •o(+C7-C„+o -1990=, 0-199 0,-+o -403 C=6) ( Io) = l •o(+05 — 05 — 0,4-1^0 -060 0,.; — O -500 Oae) (ii) = i •"( |-0„-C„+C,4+o-o97 0.6) 4192 — No. 7 — 02 6 I 82 THE EASTERN OBLIQUE ARC. Equations of conclati2is. B3 l_ C, C2 C3 C4 C5 C6 C7 C8 C9 Cio •C.i C12 C13 C14 C15 C16 C 7 C,8 c. I 0- = +0-037 + 2 + 1 2 -0-225 + 6 + 3 — 1 + 2 -2 +2-144 3 —0-219 +6-1 + 2-1 —2 -2-1 +2 —2 — o'o664 4 —0-411 +6-3 +2 — 2-| —2 —0-8004 5 -0-367 +6-2 — 2 -2-2 —2 "2 —0-069 6 + 1-410 +6-7 +2-4 —2-2 + 2-4 +0-S004 7 +0-733 + 6-7 -2 + 2-4 -2-3 +0 -665 8 -0-2S4 +6-3 — 2-1 <; + 2-497 + 6-4 -2 + 2 +2-2 10 I r -4-22S + 2-331 +6- — 2 + 6-8 +2-3 -0-665 12 13 + 1-971 + 4-35' +6.7 -2-1 +2-1 + 6-4 -2-1 14 + 2-295 + 6-5 -2-2 I,S +0-154 + 6-3 -2 + 2- 1 —21 16 -.■831 • +6-1 + 2 17 -1-313 +6- I —2-1 18 -0301 +6-9 '9 +0-152 +3 ■4907'^ 20 + 3 '"24 21 + 9 '942 22 + 0436 23 + 2-004 -M -0-915 25 + 2-359 26 -2-/92 27 +0 -463 28 + 1 -619 29 0- = +5-491 C=5 C=6 Cj3 499 3316 541 560 2834 499 510 954 499 +0 -954 -67287 ■05354 0-091 5-5261 5 '435 1 0226 6 5145 2-217 9-2112 - 0-317 + 2 -7384 + 0-8384 - 4-17989 — I -69S02 + 180-71371 + 0-140 +0140 -0'565 — I 2822 o -838S +0 -8384 + 1 -32S9 +0 -5772 -0-S384 +0-5772 +0 -0749 — o -00364 +0-20656 -7-33772 + 2-14648 +0-917 +0-917 +0-3144 -2-2596 +0-917 + 1 -706 -o '0424 —0-726 +2-2596 +0 -63365 +4-86502 +0-31545 + 1 -19985 +8- 91 109 -0 '692 +0 -306 -0-692 +0-306 +0-4776 +0 -9764 +0-692 — 00669 +0-1067 — I -2408 + 1 -240S —0-47817 -0-34531 +6 -37872 + 0-95026 -0-63456 +4 '82271 +0 -306 +o'3C'5 - -7596 +0'6oi2 — 0-690S +0-7615 - o -690S + 0-21 145 + 0-15269 + 0-10526 +0 -00025 -2 "01060 + 1 -78SS6 - o -500 + 0-1742 - 2 -6S29 ' + 0500 - 3-9684 - 4-2876 + 0-145 + 6-3885 - 6-0335 + 2-6829 + 0-2627S — 0-02717 — 2 -70072 + 0-1319S +S6 -73579 -0-2453 +0-82605 -0-8:14 '-0 '03755 —0-17685 +0 -45004 + 3 03127 + 2-4560: + 3-96849 + 3-96849 - 6 49242 + 5 '79582 - 0-0035 - 06971 - 2-06877 + 3-96S49 + 3-96849 - 6-25471 + 6-25471 - 0-24247 + 2-5316 - 2-45607 — 0-30010 — 0-29917 + 2-2lS04 + 2-jiSo4 -89-58581 -87-90629 - 0-21348 + 0-41457 +94 -10164 +91 -42321 +9S -45205 84 THE EASTERN OBLIQUE ARC. Resulting- Correlates. Ci =— 0-II5 09 c,i=+o-o83 78 C2, = — 0-137 98 Co =+0-193 iS C,2=— 0-350 90 Cij=— I -132 88 C3 =-0-071 44 C„=---o-982 35 C23=+o-952 70 C4 =4-0-110 00 C,j= -1-30571 C24 = +o-3S3 71 C5 =-0-378 51 C,5=-o-85i 29 C,5=-i-o46 58 Ce =-0-337 23 C,6=-o-234 29 C:;6=+o-755 58 C7 =+0-050 86 C,7=+o-978 52 C27 = +o-6S9i5 C8 = -0-362 70 C:8=— 0-131 58 C28= + I'339 40 C9 = + 0-411 93 C,9=+o-o8ooi C2Q=— 0-677 99 C,o = +o-255 74 C2o= — 1-72674 and resulting corrections to observed directions: (I) = = -0-1151 (ii) = = — -6010 (21) = = -0-8348 (31) = = -t-i -3112 (2) —0 -0781 (12) +0 -0825 (22) +0-0159 (32) -0 -2437 (3) +0-1932 (13) —0 -8262 (23) +0 -6689 (33) -0 -3526 (4) —0 -1 144 (14) + -2901 (24) +0-9164 (34) +0 -S473 (5) +0 -0255 (15) +0-2258 (25) +0 -5286 (35) -0-3136 (6) -0-1304 (16) +0 -0491 (26) —0-2729 (36) -0 -2452 (7) +0-2194 (17) +0 -1102 (27) -I -1311 (37) —0 -6491 (8) +0 -3708 (18) -I '0555 (28) -0-2745 (38) -0 -3747 (9) +0 -9042 (19) +0-5427 (29) —0 -8561 (39) +0-9150 (10) +0 -0695 (20) —0 -1826 (30) -0 -3963 (40) +0 -6273 (41) = =+o-ii86 (48) = = +0-5984 (42) — I -4084 (49) -0 '5995 (43) +0 -2994 (50) + 1 -8370 (44) +0 -2284 (51) —0 -0606 (45) +0-7526 (52) — I -1669 (46) +0 -5424 (53) -0-7156 (47) -0-5413 We have the probable error of a direction of unit weight 0-674 /-!=^--^ = o'674 /"'^-^ or dz o"'62 nearly, and since the average reciprocal of the weights is I '07, the probable error of an observed direction is nearly ± o"'65. T.ASK LINKS AND I'.ASK NETS. 85 No. h'csiilliii^ oil i;/i-s and sidrs iif lln ■ Allan h / hasf II ■/. Btatioiis. observed angles. Correc- tion Spher- ical angles. Spher- ical excess. \/i%. dis- tances. Di.stances in meters / // // // // Stone Mountain 3' 26 36 -633 — -404 36 229 0-1.-8 3 -970 276 I 9 338 -478 Atlanta vSouthwest Base 65 44 2 2 -204 +0 -334 22 -538 0-I28 4 -212 738 2 i6 320 -68 Atlanta Northeast Base 82 49 01 -328 +0 -289 01 -617 0-128 4 -249 47" 6 '7 761 -13 Stone Mountain 14 3" 01 -368 -0 '068 01 -3(X) -062 3 -654 412 4 5 ' 2 -446 Atlanta Southwest Base 65 44 22 -204 ho-334 22 -538 -062 4-215 648 2 16 430 -40 Atlanta Middle Base 99 45 36 -656 -0 -308 36 -348 -062 4 -249 470 5 '7 761 -13 Stone Mountain 16 56 35 -265 -0 -335 34 -930 '066 3 -683 590 2 4 826 032 Atlanta Middle Base 80 14 23 -381 +0-271 23 -652 -066 4-212 738 2 16 320 -68 Atlanta Northeast Base 82 49 nl -328 +0 -2S9 01 -617 -067 4 -215 648 .3 16 430-41 Sweat Mountain 21 37 55 -366 +0 -652 56-or,S -192 3-970 276 I 9 338 478 Atlanta Northeast Base 74 08 33 '323 -0-301 33 -022 -192 4 -386 815 7 24 367 -76 Atlanta Southwest Base 84 13 31 '520 +0 -016 3' -536 -192 4-401 456 3 25 203 -24 Sweat Mountain 12 36 3 1 -673 — r -099 30 -574 0-184 4-249 470 6 '7 761 -13 Stone Mountain 17 25 34 743 + 1 -160 35 -903 0-184 4 -3S6 S15 7 24 367 -76 Atlanta Southwest Base 149 57 53724 + 0-350 54 -074 0-183 4 -609 S72 2 40 726 04 Sweat Mountain 9 01 23 ■ 693 + 1 -752 25 -445 0-136 4-212 738 2 16 320 -68 Atlanta Northeast Base 156 57 34 '65 1 —0 -013 34 -638 " '1 37 4-609 872 2 40 726 -04 Stone Mountain 14 01 01 -890 - 1 -564 00 -326 0-136 4 -401 456 3 25 203 -24 Academy 42 29 26-166 + 2 -552 28-718 -290 4 -212 738 2 16 320 -68 vSlone Mountain 70 44 29 -036 +0 -768 29 '804 -290 4 -358 "7 9 22 809 -61 Atlanta Northeast Base 66 46 01 -440 +0 -908 02 -348 -290 4-346 400 3 22 202 42 Academy 23 GO 36 ■521 - 1 -897 34 -624 -337 4-40! 456 25 203 -24 Atlanta Northeast Base 136 16 23 '909 -0 -S96 23 -013 -336 4-649 026 S 44 568 -38 Sweat Mountain 20 43 03 -077 +0 -296 03 -373 -337 4 -358 117 9 22 809-61 Academy 65 30 02 -687 +0 -655 03 -342 0-763 4-609 872 2 40 726 -04 Stone Mountain 84 45 30 -926 -0 -796 30 ■ '30 -763 4-649 026 8 44 568 -38 Sweat Mountain 29 44 26 770 + 2 -047 2S-SI7 -763 4-346 400 3 22 202 42 Kenesaw T4 47 22 -271 +0 -064 22 -335 -1 85 3 -970 276 1 9 338 -48 Atlanta Northeast Base 46 34 26 -983 +0 -534 27-517 0-185 4-424 374 S 26 568 -98 Atlanta Southwest Base iiS 38 10 -842 —0 -140 10 -702 -184 4 -506 615 3 32 108-15 Kenesaw 16 32 34-561 — 1 -2S1 33 -28i) "•343 4-212 738 2 16 320 -68 Atlanta Northeast Base 129 23 28 -3 1 1 +0 -822 29-133 " -344 4-646 394 5 44 299-06 Stone Mountain 34 "3 58-891 —0-274 58-617 " -343 4-506 615 3 32 l(V> -15 Kenesaw 1 45 12 -290 - 1 -346 10 -944 -030 4-249 470 6 ,7 761 -13 Atlanta vSouthwest Base 175 37 26 -954 -0-194 26 -760 -031 4-646 394 5 44 299-06 Stone Mountain 2 37 22 -258 +0-130 22 -38S -031 4-424 374 S 26 568 -98 I, 86 THE e:astern oblique arc. Resultiyig angles and s/drs of the Atlanta base net -continued IS. Observed angles. ^°TJ^ Spher- ical Spher- ical angles, excess. I5 '630 i-o"503 '6-133 ' •,3«3 4 -587 666 5 3« 696 -04 6n 58 46 -044 ') '433 45 '6" ■ ■3«3 4 -65' 920 I 44 866 -28 47 21 35 755 I '140 34 •615 -918 4 -5 '9 739 5 33 r)93 -26 46 5" 26 -339 ,-() -044 26 -383 -918 4-516 084 1 32 815 -89 ^5 4S on -814 +0 -942 "I 756 -9 1 8 4-651 920 I 44 866 -28 43 29 35 -631 -|-o-o7r 35 702 -889 4-519 739 5 33 093 26 95 ( ):^ 54 -068 -1 0-153 54-221 -889 4-680 2S4 r 47 •"'94 -33 4' 26 32 -604 +0-140 32 744 -889 4-502 751 9 3' •"123 79 43 12 01 '400 . +0 -453 01 -853 0-931 4-516 084 1 32 815 -89 44 21 28 -210 -f -802 29 012 0-931 4-525 240 9 33 515-13 92 26 31 -871 +0 -058 31 929 0-932 4 -680 284 I 47 S94 -33 S6 41 37 "031 +0 -524 37 '555 0-903 4-651 920 I 44 866 -28 48 13 27 729 +0-109 27 -838 -902 4-525 240 9 33 5'5-i3 45 04 56-116 -hi-igS 57 -3 '4 -902 4-502 751 9 3' 823 -79 31 09 48 -202 1 -290 4-502 751 9 3' S23 -79 5' 39 33 '335 - 1 -637 31 698 I -290 4 -6S3 359 5 48 234-69 97 10 43 "359 +0 -612 43 '971 I -291 4 -785 444 9 61 016 -17 29 48 57 '408 0-995 4 -525 240 9 33 515-13 115 oS 5S '577 -1 -142 59719 0-994 4 -785 444 9 61 016 -17 35 02 03 696 ^-2 -161 05 -857 0-995 4-5S7 666 5 3S 696 04 26 33 40-511 -352 4-6S0 2S4 I 47 >*^94 -33 S 09 57 704 — I -70S 55 '996 -352 4-182 214 9 15 213 -oo 145 16 24 '035 + 0-513 24 '548 0-351 4 -785 444 9 61 016 17 {Kene.saw Pine Log Grassy 1 Kenesaw Grassy Sweat Mountain Descriptions of stations. Atlanta Soutlnccst Base. — This station is in De Kalli Count\-, Georgia, about \2 miles northeast of Atlanta, near and to the east of the track of the Southern Railway. It is sitttated on the northwestern .slope of a small hill, 20 meters from and S feet lielow the summit. It is 100 meters south of Humphrey's hou.se. This end of the base has both a surface and an uiulerorouiul mark.. The lower mark is a hole drilled in a copper bolt in the top of a granite po.st 2 feet long and 6 inches square. The top of this po.st is 3>^ feet below that of a large granite monument covering it, the upper mark being in this ujiper monument. The upper block is 3-3 feet .square at ba.se and 3 feet .square at top and 2-5 feet high; it rests on a brick platforin. laid in cement, 5 feet square and i foot high, with hole i foot square in center, through ■which the top of lower monument may be seen. A drill hole at the intersection of two 88 THE EASTERN OBUOUE ARC. cross lines, in a copper bolt driven into the center of the top of the upper block, marks the station. Over the upper monument is placed a granite shaft bearing the usual inscriptions on its faces. The station is further defined as the center of a square whose side is 24"' '75, each angular point of the .square being a drill hole at the intersection of cross lines in a copper bolt driven into the top of a stone post 3 feet long and 6 inches .square at top. The center of each reference mark is 18 meters from the station, and diagonal grooves are cut in top of each, with an arrowhead pointing to the station. Atlanta Northeast Base. — This station is at a road crossing on the Southern Rail- wa\-, near Norcross, Gwiimett County, Georgia. It is on the west side of the road and the west side of the railroad, on the place of J. H. Maloney. The station is marked exactly as described at Atlanta Southwest Ba.se. Atlanta Middle Base. — The .station is in De Kalb County, Georgia, upon a .small knoll in edge of woods 65 feet northwest of the Southern Railway and about a quarter of a mile northea.st of the railroad .station at Doraville. The underground mark is the center of the mouth of a .short-necked bottle. The surface mark is a drill hole at the intersection of cro.ss lines in the head of a copper bolt driven into a granite post, i foot square and 3 feet long, with diagonal grooves cut in the top, one in line with the base and the other perpendicular to it. The copper bolt with the cross lines and drill hole is placed at the intersection of the grooves. Aroinid this central monument are l:)uried four reference marks, two in line with the base and two in a line perpendicular to it. Each of the granite posts is 7 inches square and 3 feet long, and has in its top a diagonal groove with an arrowhead pointing to the station, from which the center of each reference mark is 5 feet di.stant. Stone Moiintajji. — This station is in De Kalb County, Georgia, on the well-known movuitain of that name, about 15 miles N. '76° E. from Atlanta, and al)out i mile from the po.st-office. Stone Mountain, on the Georgia Railroad, De Kalb County, Georgia. The .station is marked by a copper bolt in the solid granite of the mountain. Around the bolt the rock is cut down to a- level in a circle of ■XiV'^ f^^^t radius, the bolt being the center. In the periphery of this circle are six equidistant holes 2,y2 feet apart and 2 inches deep. Acadeiny. — This .station is on the highest point of Academy Hill, in Lawrenceville, the county seat of Gwinnett County, Georgia. The underground mark is the mouth of a bottle 3 feet below the surface. Over this is a granite po.st 30 inches long and 7 inches square, with the letters U. S. C. S. cut in top. Arotuid the central monument are placed four reference marks about 30° W. of S., 30° N. of W., 30° E. of N., and 30° S. of E. The center of the SW. reference mark is 4 feet 6 inches from the center of the station, and the center of the other marks is 5 feet di.stant from .station. In the top of each reference mark is a diagonal groove with an arrowhead pointing toward the station. A?;;f.sc77£'.— This station is on the highest part of Kene.saw Mountain, about 3 miles northwest of Marietta, Cobb County, Georgia. The station is reached by following the Marietta and Cartersville road for about 2>^ miles from the Kenesaw House, in Marietta, and then following the road which turns to the left, near a covered well, and finally along the spur of the mountain to the .sununit. The underground mark is a cross in the head of a copper bolt driven into a hole drilled in the .solid rock 2 feet i^^ inches below the surface. Above this is planted a granite po.st 5 inches square, with BASE LINES AND BASE NETS. 89 f I the top projecting 2 inches alxjve the ground. The intersectif)n of two cross lines in the top of the post marks the station. Tlie letters U. vS. C. .S. were also cut in top of post. The station has three reference marks A, B, and C — these being the intersec- tions of cross lines cut in the heads of copper bolts driven into holes drilled in the rock. The distances of these points from the .station are 6'65 feet, i i'35 feet, and ii'iy feet, re.spectivel}-. The angles subtended at the .station by lines from A to B, B to C, and C to A are 170° 59', 47° 06', and 141° 55', re.spectively. Sweat Mountain. — This station is in Cobb County, Georgia, the nearest post-office being Woodstock, almost 4 miles distant in a direct line on the Atlanta, Knoxville and Northern Railroad. The station is ow top of the mountain, about i )^ miles from Mr. Dial's hou.se, and is reached by following the Marietta and Cunnning road to a point 9^ miles from Marietta, near Mr. Garri.son's, and then taking the road along the southeast ridge of the mountain. The station is marked by a copper bolt driven in a hole drilled in the rock very near the edge, and has three reference marks, A, B, and C, which are copper bolts driven in drill holes in the mo.st solid rocks available. The.se points are 6"2 feet, 7 '67 feet, and I2"3 feet, respectively, from the .station. Taking the line to Kenesaw, vS. 48°33' W., a.s the initial or zero direction, and measuring angles counter-clock-wise, the directions of A, B, and C are 3° 19' 30", 83° 44' 30", and 231° 12' 30", respectively. Sawnee. — This station is on the most prominent or central peak of vSawnee Moun- tain, in Cumming Township, Forsyth County, Georgia, about 2 miles NH. of Cumming and 12 miles from Buford, on the vSouthern Railway. The station was marked temporarily by a copper tack driven in a stul), with similar stubs for reference marks. The permanent marks are supposed to l)e the usual central ( marks with four reference marks. Pine Log. — This .station is on Pine Log Mountain, Cherokee County, Georgia, about 7 miles north of Wolf Pen. The station is reached by going east from Carters\-ille, a, to Wolf Pen; thence 9 miles to Moore's Iron Furnace; thence 3 miles to Mr. Lewis' house; thence to the station on top of the mountain. The underground mark is the neck of a jug 2 feet 6 inches beneath the surface. The surface mark is the intersection of cross lines on the top of a granite post 5 inches square, planted above the jug, the top of post projecting above the ground. The letters U. S. C. S. were cut in the angles of the cro.ss lines. Around the station are four granite reference marks .similar to the central monument, to the north, east, .south, and west, each distant 6 feet from the station. In the top of each is cut an arrowhead pointing to the station. Grassy. — This .station is on top of Grassy Mountain, 3,290 feet high, in Pickens County, Georgia, about 6 miles in a direct line east of Jasper, the county seat, on the Atlanta, Knoxville and Northern Railroad. The station marks are supposed to be the usual central moiunnent, and four reference marks to the north, east, south, and west, each 5 feet distant from the station. I 1 I 90 THE EASTERN OBLIQUE ARC. 6. THE DAUPHIN ISLAND BASE LINE AND BASE NET, ALABAMA, 1 847. Locatio)!, iinnsKrcim )t/, and rbscrvation equations. o=-i-oo-(3) + (4)- (5)+ (7)- (8)+ (9) o= + i-25-(i)-f{3)- (9) + (io)-{ii) + (i3) o=-fo-76-(2) + (4)- (5)-f (6)-(i4) + (i5) o=-o-65-(i) + (2)-(i2) + (i3)--(i5) + (i6) o=-o-4 +1 •63(i3)-2-93(i2) + i -30(11) | i -66( 10 1-4 •38(9) + 272(8)-o-52(7)-|-2-i6(5) — I •64(6)+o-27(i6)-{ o-65(i5)-o-92( 14) BASE LINEvS AND BASE NETS. 97 The solution of the normal equations j^ives the values of the correlatives: and the corrections to the directions are: c,= +0 •2645 c,= — -2234 C3 = — •1617 C4 = +0 •0783 C5 = +0 -0726 ctions are: // // (i) = = +o-i45 (9) = = +0-170 (2) +o -240 (10) -0-103 (3) -0 -488 (II) +0-318 (4) +0-103 (12) —0 -291 (5) +0 -054 (13) —0-027 (6) -0-281 (14) + 0095 (7) +0-227 (15) -0-193 (8) —0 -067 (16) +0 -098 The mean error of a direction,./ — Z3 = -(-o'' -38 and the probable error=^o" -26. Kc'sulthti^ ang/t's and sides 0/ the Dauphin Island base net. stations. Obse rved angles. Correc- tion. »pneri- ical angles. ^»pneri- ical excess. I.og. dis- tances. Distances in meters. / // '/ // // Cedar Point ' 37 43 12 -90 +0-24 13 '14 -09 4-027 832 I 10 661 -83S Dauphin I'd. East Base 103 52 29-53 +0-17 29-70 -10 4-228 357 16 918-31 Dauphin I'd. WestBase 38 24 16-86 + 0-59 17-45 -10 4 -034 45S 5 10 825-76 Point aux Pins 58 14 08 -33 -0 -35 07 -98 -21 4 -228 357 16 918-31 Cedar Point 51 42 20-35 —0 -27 20 -08 -21 4 193 605 I 15 617-27 Dauphin I'd. West Base 70 "3 33 '20 -0-63 32-57 -21 4-271 975 5 1 8 705 -77 Cat Island 66 28 28-62 — -29 28-33 -08 4-027 S32 I 10 661 -84 Dauphin I'd. East Base 52 04 29-67 -0 -33 29-34 -07 3 -962 492 9 9 172 -61 Dauphin I'd. West Base 61 27 02 69 -0-I4 02 -55 -07 4-009 213 8 10 214-42 Point aux Pins 35 37 34 -88 t -26 35-14 09 3-962 492 9 9 172 -61 Cat Island 97 21 37 '37 +0 -29 37-66 -09 4-193 605 2 15 617-27 Dauphin I'd. West Base 47 (X) 47 '37 +0-10 47-47 -09 4 061 419 I II 319 -I I Fort Morgan (1S47) 50 44 14-6 +0-1 14-7 -2 4-228 357 16 918-31 Dauphin I'd. West Base 47 21 43 ■" +0-2 43-2 0-2 4 -206 '43 7 16 074 -73 Cedar Point 81 54 02 -6 +0-2 02 -8 "■3 4 -335 1 20 3 21 633 -17 Descriptions of Stations. Daup/i/n hla>id East Base. — This station is on Dauphin Island, at the entrance of Mobile Bny about 7 miles from the west end of the island and 352 miles from the east end, near the western edge of the pine woods which cover the ea.stern end of the i.sland. The -Station was recovered and reoccupied in 1S97 and marked as follows: In a bed of cement 5^ feet .stiuare, extending 6 feet below the surface, are two 4192 — No. 7 — 02 7 98 THE EAvSTERN OBLIQUE ARC. pieces of drain tile 2 feet long and 4 inches in diameter, each placed with its axis vertical, one above the other, the lower extending 7 inches below the bottom of the cement. A pine pole 6 feet long and 2 inches in diameter is driven down through the pipes until its top is 16 inches below the top of the upper tile. Above this pole in the upper pipe are placed vertically, one above the other, two copper bolts, each H inches long and 3'/( inches in diameter, a cross on each bolt marking the station, the upper mark beings feet l)elow the surface. The bolts are held in place by cement, with which the remaining space of the pipes is filled. Above the top of the upper pipe a cavity i foot square and 6 inches deep is left in the cement. Over this cavity, still embedded in cement, the four original granite blocks of the base of the monument of 1847 are built, as originally, in two courses, the top of the upper course projecting 2 inches above the surface. A copper bolt in the top of one of the blocks of the upper course is directly over the cross on tlie bolt in the pipe and marks the station. Tlie original granite shaft is placed on this foundation and cemented down over the copper bolt, its apex again marking the station. On the north, east, south, and we.st faces of the .shaft are inscribed, respectively, "A. D. Bache, Siiptdt.," " U. S. Coast Survey," " 1847," " Base No. 5." The station is witnessed by two marks in the same vertical line, one on the surface and one underground, in prolongation of th^ base line, 144' 1025 meters east of the extremity and just in the edge of the pine woods. The underground mark is a cross in an iron bolt in the top of a tile pipe 2 feet long embedded vertically in a mass of cement 2 feet in diameter, the top of the pipe being 3 feet below the surface. Above this ])ipe is placed a granite block i foot square and 2^^ feet long, the top of block being flush with the surface and containing a copper bolt as the surface mark. Dauphin Island U^esf Base. — This station is on the western end of Dauphin Island. In 1847 the station was within one-half mile of the extremity of the island, while in 1897 the island extended 3^2 miles west of it. In September, 1897, the distance was reduced by a storm which wa,shed away i mile of the western end of the island. The station is marked as described at Dauphin Island East Ba.se, except that the cement at this .station is 6 feet square and 5 feet deep and only one piece of tile pipe was put in. Fori Morga)i. — The station is near the center of the northwest bastion (No. 2) of Fort Morgan, at the entrance to Mobile Bay. The station of 1S46 was recovered and reoccupied in 1892 and again in 1897-98. The earthenware vessel u.sed originally was left in its place, filled with cement, and a nail was placed in its center to mark the station, the top of the nail being 2^ feet below the surface. Aliove this was placed verticallj' a section of tile drain pipe inclosed in a nail keg, both filled with cement. In the pipe are two spike nails, one above the other, making additional marks. The head of the upper nail is just beneath the brick floor. Cat Island. — This station is on Cat Island, in Mississippi Sound, north of Dauphin Island. The station of 1845 was marked by a buried earthenware cone. In 1855 a new station was e.stablislied near the old one. Cedar Point. — This station is on Mon L,ouis Island, on the western .side of Mobile Bay. The station is situated on the ea.stern extremit}' of the island, on a narrow strip of Ijeacli, among marshes. In 1846 an earthenware cone was buried as the station mark, and copper nails were driven in blazed trees with the following directions and distances: One northwest, 9 feet 4 inches; one northeast, 18 feet; one southwest, 32 feet 6 inches, as reference marks. BASE LINES AND BASE NETS. 99 Point aiix Pi)is. — On the point of land of the- same name which extends southward into Mississippi vSound, just west of Bayou Batture. \\\ 1X46 the station was marked by an earthenware cone buried 3 feet under the surface. In 1848 four poles 4 feet lon^ and 6 inches in diameter were inserted around the undisturbed cone, the station being the point of intersection of two perpendicular lines determined by four copper nails driven in the tops of these poles. St. Elmo. — The .station is in Mobile Count}', Alabama, about 2 miles east of St. Elmo, on the Louisville and Nashville Railroad, and about one-half mile south of Otis' s mill. The station is in the northwest corner of N. E. yi of S. E. Yx of S. E. ){ of 1 S. E. ;^ of N. W. X' •''Cc. 19, T. 6 S., R. 2 W., and is distant from the northwest corner of section 19, 3426 feet, and bears from .said corner 313° 43' true. The underground mark is the intersection of cross lines on top surface of limestone post, 6 inches square and 18 inches long, buried vertical!}-, with top 3 feet below surface ^ of ground. The letters U. vS. C. G. S. are cut in the angles of the cross lines. Six * inches above this is another limestone po.st, 6 inches square and 28 inches long, its top level with the surface of the ground and marked as the lower stone. Daphne. — This station is in Baldwin County, Alabama, about one-half mile northeast of the court-hou.se at Daphne. The station is in the southwest corner of the S. W. ^ of S. W. % of N. E. Yx of N. E. Y\ of N. E. Ya^ sec. 19, T. 5 S., R. 2 E. Distance from the northeast corner of section 19 to station is 882 feet, and the station bears S. 44° 17' W. (true) from the northeast comer of section 19. A I -gallon stone jug was buried, bottom up, and a small hole in the center of the {bottom, 3 feet below the surface, is the underground mark. A limestone post 6 inches square and 30 inches long was placed in a vertical position 6 inches abo\-e the jug, the surface mark being the intersection of cross lines on its top surface, which is flush with the ground. The letters U. S. C. G. S. are cut in the usual manner in the angles of the cross lines. Sprhig Hill. — The station is about 7 miles northwest of Mobile, on the highest part of Spring Hill, on the land of Judge H. Anstell, about 40 feet north of the fence line of main road and about 200 yards west of road going to \^'histler, and also about 200 { yards west of station Spring Hill on electric road. The station is marked as Daphne, except that the jug is buried mouth up, the center of mouth being the underground mark. The following true bearings and dis- tances were measured: Oak tree, No. i, N. 62° 33' 10" E., 103 feet; oak .stump, No. 2, N. 18° 17' 20" W. , 39 feet 9 inches; oak .stump, No. 3, vS. 95'' 46' 25" W.. 44 feet 7 inches; fence line, S. 29° 47' E., 39 feet 11 inches. lOO THE EASTERN OBLIQUE ARC. C. SYNOPSIS OK THE MEASUREMENTS AND RESULTS OF THE BASE IINES OF THE OBLIOUK; ARC. Name of line. Date of measure. Chief of party and observer. No. Epping Base Me. 1357, July and Aug. A. I). Baclie Massachusetts Base Mass. 1844, Sept. to Nov. E. Blunt Fire Island Base N. Y. 1834, Aug. to Oct. F. R. Hassler Kent Island Base Md. 1844, May and June J. Ferguson I 1872, Nov. and Dec. | 1S72, Dec. and 1873, Jan. [C.O.Boutelle 1S73, July and Aug. J 1847, May and June A. D. Baclie Dauphin Island Base Ala. Name of line Epping Base Massachusetts Base Fire Island Base Kent Island Base Atlanta Base Dauphin Island Base .Apparatus used. Bache-Wiirdemann Hassler Hassler Hassler Bache-Wiirdeinann Bache-Wiirdemann Resulting length Logarithm of .'Approximate inme'ersand preceding num- probable error in probable error . bers. terms of length. 8 715 -9422 3-940 314 34 ± 158 ± 79 17 326-3763 4-238 707 74 d= 35S ± 90 14 058 -9709 4-147 953 53 ±585 ±1 81 8 687 -5446 3 -938 897 05 ± 680 ± 3 40 9 33S '4778 3 "970 276 09 ± 222 ± I 03 10 661 -S376 4 '027 832 06 d= 260 :±: I 06 „ 1 f 5?0 4^T0 I¥ u 15 8 1 ■J'S'T (» I I PART II. THE MAIN TRIANGULATION. THE MAIN TRIANGULATION BI-:T\V1:i:\ TIIH BAMi LINES OR NliTS. A. GENERAL TREATMENT OE THE REDUCTION OF THE MAIN TRI- ANGULATION BETWEEN CALAIS, MAINE, AND NEW ORLEANS, LOUISIANA. Since the earl}- and partial publications of preliminar}' results of the various parts of this triangulation, as referred to in Part I, changes have taken place, not only in the field work by additional stations or measures, but also in the office work of compu- tation in respect to the general treatment, and due to the experience gained in the meantime. Nevertheless, it was desirable to retain as much as possible of the older reductions, such as the computations of the base lines, the local adjustments of the horizontal directions, and the adjustment of the base nets. That part of the oblique arc which is in common with the arc of the parallel of ^ = 39° is retained unchanged. When dealing with the treatment of the portion of the oblique arc traversing the New England States, it became neces-sar}' to introduce the station Mount Washington, New Hampshire, into the scheme, and to consider the most advantageous manner l)y which the three base lines (or their nets), the Epping, the Massachusetts, and the Fire Island bases, could be brought into perfect accord. This was to be done with due regard to the labor involved in the establishment and .solution of a large number of equations. At the same time attention had to be given to the circumstance of the intersection of the oblique arc with a triangulation, now nearly completed, which can be u.sed for the discussion of an arc of the parallel, in latitude 42^4°, from Cape Cod to the State of Iowa, executed partly by the U. S. Lake Survey and partly by the U. S. Coast and Geodetic Survey for this and other purposes. Further, attention had to be given to non-interference with the full development of the large triangulation in the States of New Hampshire and Vermont, which has Killington, Vermont, as a central station. After due consideration it was decided to retain unchanged the adjustment of the Epping base net as made in June, 1864, and to adjust the triangulation between the three bases, so as to preserve the length of the side Humpback to Mount De.sert (of the Epping base net), the Massachu.setts base, and the side Wooster to Sandford (of the Fire Island base net). This scheme involves the simultaneous solution of 57 equations, two of which are length ecpiations, each containing a large number of terms. The results from the old but less perfect scheme differ very little, and within the imcertainties of the measures, from tho.se now obtained, and also indicate the excellent accord of the relations of the newly added station to the surrounding stations. The small extension of the Epping base net from the side Cooper to Howard to the boundary on the St. Croix River was afterwards treated by itself. The .stretch of triangulation between the base nets of the Fire Island base and the Kent Island base starts from the line Bald Hill to West Hills, and ends on the line 105 I04 THE EASTERN OBLIQUE ARC. Osbornes Ruin to Turke\- Point, and the latter line, being a part of the adjusted triangu- lation of the arc of the parallel in (^=39°, is preserved as given in Special Publication No. 4, " The Transcontinental Triangulation. " The adjustment involved the solution of 35 equations, of which the conditional or observation equation for accord of length of sides contains 89 terms. The triangulation lying between the line Osbornes Ruin to Turke}' Point, Maryland, and the line Tobacco Row to Spear, Virginia, is retained unchanged as given in Special Publication No. 4. Upon reaching latitude 36° the triangulation splits into two branches, one, the western and later one, passing through Tennessee, the other and older one through North Carolina. They unite again in northern Georgia. The angular mea.sures on the western branch were made with an inferior instrument. A study of the local adjust- ments of this triangulation and of the approximate computations which were available indicated that the angle measures did not pos.se.ss quite the .same accuracy as those of the eastern branch and could lend no additional value to the triangulation to the .south- ward. Moreover, there are no astronomic ob.servations of any kind connected with this triangulation. For these rea.sons the western or Tenne.s.see branch was not used as a part of the arc, and the computation between the Kent I.sland and Atlanta bases was carried through the ea.stern branch. Proceeding southwestward from the line Tobacco Row to Spear to the Atlanta base, the adjustment was made in three parts. The complex strong figure between the lines Tobacco Row to Spear and Buffalo to Moore was first adjusted and involved the .solution of 24 equations. The influence of the Atlanta base was then extended by the adjustment of the section of the triangulation from the line Sawnee to Gras.sy to the line Benn to King, involving the solution of 41 equations, and finally the remaining portion, forming a central figure about the station Poore, was adjusted, involving the .solution of 13 equations, including a length equation introduced for the purpose of bringing the lengths derived from the two bases into accord. The reasons for dispersing the small outstanding discrepancy in this particular figure are given in the portion of this publication which treats of its adjustment. The fortunate circumstance that the Atlanta and the Dauphin Lsland bases, when connected through the chain of intervening triangles or more complex figures, proved to be in almost exact accord, as was shown by the .several adjusted pieces of triangulation gradualh' joined together as the field work progre.s.sed , made it possible to retain all of these five partial adju.stments. This carried the results to the Dauphin I.sland base net at the line Spring Hill to Daphne. It was thought highly desirable to extend the ol)lique arc as far as the city of New Orleans, where it meets with and terminates at a well-determined a.stronomic .station. It was known that the small coast triangulation along the Gulf from Mobile Bay west- ward was inferior in accurac>' to first-class work. Nevertheless a rediscu.ssion and new adjustment showed that it could be used to extend the arc to New Orleans. The whole of this triangulation is old, and the inferiority of the work is due to the difficulties encountered on account of the climatic conditions along the Gulf coast, and particularh^ to the effects of .severe hurricanes passing across this region, which rendered it difficult to preserve the stations from one season to another. It was also most important to include the station at New Orleans in the discussion of the local deflections of the plumb line at stations approaching and in clo.se proximit>- to the Gulf of Mexico. THE MAIN TRIANGULATIOX. IO5 B. THE TRIANGULATIOX. I. NORTHKASTKRN TKRMIXITS TO KPPING BASK XKT. The extension of the triangulation from the primary Hne Cooper to Howard, of the Epping base net, to and across the Canadian boundary at the St. Croix River is shown on the following diagram. The geometric figure is a strong one and demanded for its No. 16. 167. David Howard Kilometers 10 20 Statute Miles adjustment that 13 conditional equations l)e satisfied. Equal unit weights were given to the directions, excepting the initial line Cooper to Howard, to which a double weight was assigned. The angles measured with the repeating circle were generall>' made up of jo sets, each of three repetitions direct and three repetitions reversed for every angle: these results, when combinations existed among the measured angles, were adjusted at each io6 THE EASTERN OBLIQUE ARC. station. The probable error of an observation of an angle (3 D. and 5 2?.) is given b\ e , and that of a direction by t\ = e i /^J2. The approximate elevations of the stations above the half-tide level of the Atlantic are as follows: Chanicook Trescott Rock Prince Regents Redonbt 60 Grand Manaii Calais, oVjservatory Howard Cooper No reductions to the horizontal directions for heights were required. eters. Feet 197 647 94 3'o 60 197 I 28 420 46 150 82 269 225 738 Abstracls of rt'siiltine: horizontal diit'ciioiis obserz'cd and adjus/cd at stations of the tria7igiitation extending to the Canadian boundary, jS§g to /S6/. Hoivard, A. D. have: Washington County, Maine. July and August, 1S59. 75'='" direction theodolite No. i. Bache and G. W. Dean, ob.servers. P'roni abstract given in Part I of this publication we No. of directions. < )bjects observed. Resulting directions from .station adjust- ment. Corrections from pre- ceding fig- ure adjust- ment. Resulting directions. Corrections from pre.s- ent figure adjustment. Final seconds. Pigeon Cooper Trescott Rock Grand Manan o CXI 00 '000 — o'oS9 00 '000 108 01 27 '996 --0 '066 173 43 51 '973 -0-026 1S9 28 45 -843 -o -026 Mean correction — o '026 28-018 28-018 52-036 -0-398 51 ■63S 45-906 f 0-267 46-173 Cot^/'c;', Wa,shington County, Maine. August and September, 1859. 75"^"' direction theodolite No. i. A. D. Bache and G. W. Dean, observers. 25'"' repeating theodolite No. 74. October 23, 1867. C. H. Boyd, observer. Chanicook Prince Regents Redoubt Grand Manan Trescott Rock Howard Mount De.sert Rye (Boyd)* Saint David (Boyd)* O 00 00 -QOO 38 36 49 -082 54 40 14 '493 68 43 51 -687 108 56 09 -385 157 47 00 -789 309 17 27-536 329 01 51 -167 -0 -068 00 -000 -1-0 -004 00 -000 -0 -068 49 -082 -0-951 48-127 —0 -068 •4 -493 +0 -646 15 •"35 -0-068 51 -687 -0 -058 51 '625 -0-226 09 -227 f -415 01 -272 -0 -068 27 -536 —0 -802 26 -730 -0 -068 51 -167 + 1 -117 52 -280 Mean correction — o -068 Probable error of an observation (3 D. and 3 j'?. ) of a direction, <>, * Number of sets of repetition observations, 2. THK MAIN TRIANGULATION. 107 Abatracta of rcsultinfr horizonlal dirciiions ohsicrvcd and adjusted at stations of the tria7igiilation e.vtendint,'' to the Canadian boundary, /8^g to 1861 — continued. Owwrof/', New Brunswick. October 22 to October 28, 1859. 75"" direction theodolite No. i. G. W. Dean, observer. 25"" repeatinj^ theodolite No. 74. C. II. Boyd, observer, 1867. No. of direction.s. 16 17 IS 19 Objects ob.served. Grand Manan Prince Regents Redoubt Trescott Rock Cooper --!i^!j^:;-\--' frc^^l^S;,,. UJMS justinenl. / // // 00 00 '000 ±0-139 to -491 II 23 35 -285 ±0135 -0150 28 '7 21 '691 ±0-141 — o-i6o 88 44 50-139 ±0-173 -0 -723 "5 16 24 -874 +0 -344 138 46 22 -644 +0-319 165 22 52 -991 —0-120 20 . Rye (Boyd)* 21 Calais, observatory (Boyd)* 22 Saint David (Boyd)* Probable error of an observation (3 D. and 3 K.) of a direction, c, = a single observation of a direction, e^ = ± i" -08. Trescott A'oc/c, Washington County, Maine. November i to 7, 1S61. No. 30. C. H. Boyd, observer. Final seconds. // CO 000 34 -644 21 ■040 48 •925 24 •727 22 ■472 52 •380 Probable error of 30"" repeating theodolite 1 1 Howard 12 Cooper 13 Chanicook 14 Prince Regents Redoubt 15 Grand Manan 00 CX3 -000 +0-178 oo-ooo 74 05 21 565 —0 -107 21 -2S0 124 54 05 -165 -0-173 04 814 145 27 05 -458 +0 -356 05 637 215 10 26 975 -0 -253 26 -544 Number of sets of angles, 5; probable error of an observation (3 />. and 3 R.) of a direction, ^, = ± I Prince Regents Redoubt, Washington County, Maine. October 4 to 21, 1S61. 30"'" repeating theod- olite No. 30. C. H. Boyd, observer. 23 Grand Manan 24 Trescott Rock 25 Cooper 26 Chamcook Number of sets of observations, 7; probable error of an observation (3 Jh and 3 A*. 1 of a direction. = ± I" -I. 00 00 -000 -0-371 00 000 60 06 1 2 -074 — 0214 12-231 38 37 25 265 +0-519 26-155 02 39 25 281 +0-067 25719 * Number of set.-- ot repetitiou observations, 3. io8 THE EASTERN OBLIQUE ARC. Ahslmcl^ of irsul/iui;' horiznntal directions observed and adjusted at stations of the triangulation exte)idini^ to tlie Canadian boundary, iS§g to jS6i — continued. St. David, New Brunswick. September 30 to October 2, 1867. 2^"'' repeatin.i^ theodolite No. 74. C. H. Boyd, observer. No. of directions. Objects 27 Chanicook 2S Calais, observatory 29 Cooper 3" Rye Results from station adjustment. O 00 00 '000 67 I r 50 -342 72 23 49 -293 S7 05 40 -032 Corrections from present ad- justment. -OT53 -0-319 -o '908 -o -436 Final seconds. 00 '000 50-176 50 '353 39 749 Number of sets of observations, 3; probable error of an observation (3 /?. and 3 A'. ) of a S(> 03 -49S 26-155 08 -304 27 -007 48 -924 59 "925 15 "134 21 '039 19-501 21 -730 27 '885 43 '534 5' '625 34 '643 51 -622 0-832 0-833 0-833 I "565 I '564 I '565 0-288 0-288 o -289 0-444 0-443 o -444 0-339 0-339 0-340 0-593 0-593 0-593 o -488 o -4S9 -489 1 '327 I -328 I -328 0-757 0-757 756 1 -015 I -015 I -014 o -182 o -182 4 -603 402 I 4 -580 099 7 4-430 277 o 4 -603 402 I 4-754 589 2 4 -668 845 2 4-430 277 o 4-342 006 7 4 -668 845 2 4 -580 099 7 4 754 5S9 I 4-342 006 7 4 -342 006 7 4 -289 384 2 4 '376 239 o 4 -5S0 099 7 4-565 481 2 4-289 384 2 -0-438 34-281 0-182 4 754 4-565 4 -376 4-754 4-529 4-666 4- 342 4-609 4-666 4-580 4-529 4-609 4-376 4-371 589 2 481 2 239 2 589 2 929 o 298 r 006 7 948 2 298 o 099 7 929 I 948 2 239 I 372 7 40 123-81 38 027 -67 26 932 -52 40 123 'Si 56 S31 -51 46 649-31 26 932 -52 21 978-94 46 649 -3 1 38 027 -67 56 831 -50 21 978-94 21 978-94 19 470 -82 23 781 -49 38 027 -67 36 768 -95 19 470 -82 56 831 -51 36 76S-95 23 781 -50 56 831 -51 33 878 -88 46 376-51 21 978-94 40 733 -f7 46 376-50 38 027 -67 33 878 -88 40 733-17 23 781 -49 23 516-50 4 -666 29S o 46 376 50 THE MAIN TRIANGULATION. Ill Rcsul/inff ans^lcs and sides of llu lrianv;nlalion hctivecn the lippinu; base lenitinits of the arc — continued. net and the northeastern No. i.^ 14 [5 16 17 iS Stations. Ohservei 1 anjjlfs. Correc- tion. ical angles. ical excess. I^og. dis- tances. UisUinces in meters. / // // // // Clmnicook 16 5.^ 46 '406 —0 -oil 46 '395 -235 4 -2«9 384 2 19 470-82 Prince Regent.s Re doubt 142 33 13 -207 + 0-281 13-488 0. 236 4 -609 948 2 40 7,33-17 Trescott Rock 20 33 00 -293 + o-53fJ 00 -823 -235 4-371 372 7 23 516-50 Chamcook 77 2r '4 -854 -0-574 14 -280 0-657 4-565 481 2 36 768 95 Prince Regents Re- doubt 64 01 60 '016 -0 -452 59 '564 -657 4 -529 929 ' 33 878 -88 Cooper 3« 36 49 '082 -0 '955 48-127 0-657 4-37' 372 8 23 516-51 Rye 102 45 52 -302 -0 -342 51 -960 -344 4 -529 929 I 33 878 -88 Chamcook 26 3' 34 "735 + 1 -067 35 '802 -344 4 ■I9<^' 727 15 514-11 Cooper 50 42 32 -464 +0 -806 33 '270 0-344 4-429 504 7 26 884 -67 vSt. David 72 23 49 '293 i-i -061 50 -354 0-510 4-529 929 I 33 S78 -8S Chamcook 76 3''^ 02 -852 +0 -603 03 -455 0-509 4 -538 830 5 34 5S0 -44 Cooper 3" 58 08 -833 -1-113 07 -720 -510 4 -262 199 9 18 289 -42 St. David 87 05 40 -032 -0 -283 39 749 0-319 4-429 504 7 26 8S4 -67 Chamcook 50 06 28-117 -0 -463 27 -654 0-319 4-315 000 5 20 653 -.S2 Rye 42 47 52 -302 + 1 -252 53 '554 0-319 4 262 200 18 289 -42 St. David 14 41 50 739 - 1 -345 49 '394 0-153 4-190 727 15 5I4-II Cooper '' 19 44 23-631 + 1 -920 25-55' 0-153 r3>5 000 4 20 653 -82 Rye 145 33 44 -604 +0-910 45-514 0-153 4 -538 830 5 34 580 -44 Calais Observatory 86 11 40 -903 -0 -637 40 -266 o-| 17 4-262 200 iS 2S9 -42 St. David 67 1 1 50 -342 -0-165 50-177 - 1 1 7 4-227 816 4 16 S97 26 Chamcook 26 36 30 -347 -0 -439 29 -908 0-117 3 -914 328 3 8 209 -72 2. EPPING BASE NET TO MASSACHUSETTS BASE AND TO FIRK ISLAND BASE NET, MAINE, NEW HAMPSHIRE, MASSACHUSETTS, RHODE ISLAND, AND CONNECTICUT. • 1844-1882. The main triaiigulation which connects and is based upon the three northern base lines is among the most elaborate pieces of field work ever executed b\- the Stirve\-. It was steadil}' contintted and completed by Superintendent Bache and his party in twenty years. Only one station (Mount Washington) was afterwards included in the scheme. There are also several subordinate stations, not referred to here, which, in addition to what is furnished by the principal stations, effects the junction with the subordinate, secondary, and tertiary work covering the greater part of the coast line of Massachusetts, New Hampshire, ard Maine. With the exception of the angles at the Massachusetts base, all angular directions were measured by means of the great (so called) 75"" theodolite, and the station results were deduced by application of Bessel's least .square method of reduction. The accuracy reached is quite commensurate with the amount of labor spent, both in the 112 THE EASTERN OBLIQUE ARC. Hximpbojck}. THE MAIN TRIANGULATION. 113 field and in the office. This may l)e seen in the closing errors of the 52 trianj^les as well as in the numerical constants of the 57 conditicMial equations. The first adjustment of this triangulation, made in 1866 under the writer's direction, avoided the heavy work of .solving simultaneously this large number of equations by dividing the whole work into three parts, but in this di.scu.ssion it was decided to treat the adjustment rigorously as a whole. The new results, however, differ but slightly from the older ones. The directions in the new adjustment are corrected f(jr effect of altitude of the stations sighted, and the observations made at and upon Mount Wa.shington are now incorporated into the general scheme. Approximate heights 0/ stations alwve the average level of the Atlantic Ocean. Mtters. Hect. Meters. Feel. Humpback 451 I 480 Manomet 120 394 Mount De.ser*. 465 ■ 525 Blue Hill '94 635 Mount Harris 3^^^ I 251 Beaconpole 167 54'S Ragged Mountain 397 I 301 Monadnock 966 3 1 68 vSabattus 244 Soo Wachusett 616 2 022 Mount Bhie 976 3 202 Mount Tom 372 I 220 Mount Pleasant 615 2 018 Bald Hill (Tolland County) 393 I 290 Mount Wasliington I 920 6 300 Box Hill 259 850 Mount Independence 153 501 Ivy 498 I 634 Gunstock 732 2 402 Sandford 273 S95 Aganienticus 222 72S Wooster 305 I 000 Unkonoonuc 411 > 34S Copecut 108 353 Thompson S3 271 Great INIeadovv 81 265 Ob.servation eqitation LVI is the length equation between the Epping base (referred to the line Humpback to Mount Desert) and the Massachusetts ba.se, .showing a di.screp- ancy of but 57 units in the .seventh place of decimals in the logarithms, and the corre- .sponding equation No. LVI I is the length equation between the Massachusetts base and the Fire Island base ( referred to the line Sandford to Wooster ) and shows a discrepancy of but 26 units. Weights to the 131 directions are introduced on the same principle as was done in 1866, which takes care of the circumstance that the relative weights, when the directions are combined to form triangles, are very diiiferent from and only partly resemble the weights deduced from the station adjustment alone. Experience ha.s shown that the former are at least of equal if not greater importance than the latter. The maxinuim clo.sing error in the .sum of the angles of any one triangle is but 2""o and the average closing error of a triangle, found by ,s(|uaring the 52 errors, is given by ^^^-^ 52 dro"'92; hence the probable error of a direction i.s 0*674 -_": V6 :±0 2^ = On the other hand the approximate proliable error of a direction derived from the stalioii adjustment alone"'- is foiuul from the average .sqtutre 3 '05^^ VIZ. ■, = Vo-0233 = =bo"i53; hence the .square of the combination error or «'/ = (o"255)=— (0153)== (o'204)\ To each of the values of <\', therefore, was added (o'204V' or 0*040 in order *See re.suUiiig probable errors of tlie direction presented lurtlier on with the abstraetsof the horizontal measures 4192 — No. 7 — 02 S 114 THE EASTERN OBLIQUE ARC. to get E" = -, but in order to make the average value of the 131 cases equal to uuity this was multiplied by 1575; hence the final reciprocals of weights used in the adjust- ment further on. Abstrac/s of horizontal direcfions as observed and adjusted at the principal stations betiveen the Epping base net, the Massachusetts base, and the Fire Island base net, 184-^-/882. Humpback, Hancock County, Maine. Juh- ig to September 6, 185S. 75' A. D. Bache and G. W. Dean, olxservers. direction theodolite No. i. Number of direc- tions. objects obser\ 'ed. Resulting di- rections from station ad- justment. Approxi- mate probable errors. Correc- tions from net adjust- ment. Correct- ed direc- tions. Reduc- tions to sea level. Result- ing .sec- onds. Cooper u 00 00 'OOO ±0-15 —0-196 00 -000 00 '00 Azimuth Mark 39 37 40-230 -16 —0-023 40 -403 Mount Desert 114 33 50 -877 -09 +0-583 51 656 +0 -008 51-66 3 Ragged Mountain 154 28 20 -545 0-13 — -023 20-718 4-0-022 20-74 Saunders 165 12 47-118 0-13 —0-023 47 -291 4 Mount Harris I So 36 29-988 0*17 Mean correctio —0 -023 30-161 -Ho -010 30 '17 n -0-023 Correc- tions from figure adjust- ment. -1-0 -36 Final seconds. 2973 Circle used in V positions. Mouiit Desert, Hancock County, Maine. August 14 to October 14, 1S56. 75' No. I. A. D. Bache and G. W. Dean, observers. direction theodolite Isle au Hant 00 00 "ooo ±o'i4 —0 -006 00 "000 00 -00 Ragged Mountain 33 39 21 -332 o-ii —0 -006 21 332 -1-0 -009 21-34 — -05 21 '29 Mount Harris 70 54 51 '93' 0-12 — o*oo5 51 -931 —0-017 51 -91 -ho-io 52 01 Saunders 93 48 58 -.■^82 *IO — o"oo6 58 -382 Azimuth Mark 122 49 25 '136 *10 — - 006 25-136 Humpback 144 20 00 -152 Mean '10 correction -0-143 00-015 4-0 -ooS 00-02 — 006 Circle used in "V positions. Dlount Harris, Penobscot County No. I. nner or ctions. objects Qbser\'ed. Thomas Hill, Ban- gor Azimuth Mark Peaked Mountain 5 Humpback Saunders 6 Mount Desert I.sle au Haut 7 Ragged Mountain « Sabattus 9 Mount Blue Circle used \w V positions , Maine. Jvilj' 25 to October 17, 1855. 75 '^"' direction theodolite A. D. Bacjie and G. W. Dean, observers. Resulting direc- tions from station adjust- ment. nta'te't'?mb Reductions Resulting ableer'^ot to sea level. seconds. 00 00 -000 zbOTI 1 16 32-750 0'12 9 50 32 -207 13 14 12-055 29 29 47 -495 53 46 37-3'2 85 58 21-672 118 55 14-559 170 57 33 -572 213 17 48 -992 Corrections from figure ad- justment. Final seconds. 0-13 Q-og +0-013 12 -07 —0 -QI 12 -06 Q-og 'og — -020 37-29 +0-07 37 -36 Q-II -IT "GOO 14-56 +o-o6 14 -62 -12 +0-013 33-58 — c -01 33-57 0-13 —0 "009 48-98 — o"ii 48-87 i THE MAIN TRIANGULATION. II Abstracts of horizontat directions as observed and adjusted at the princ:pat stations l^tween the Eppin^ base net, the Massachusetts base, and the Fire Island t>ase net, /^^.^-/^^.-cont.nued. • J?a^^ed Mountain, Waldo County, Maine. AukusI 9 to November 2 . , .854. 75 ' "' 'Predion theodolite No. I. A. D. Bache and G. W. Dean, oljservers. Number of directions. Objects observed. Resulting direc- tions from Reductions Kesultinf; Itingdirec- Annroxi- itis from Approxi deductions Kesumn station acSjust- ,"^tfe?rot: to sea level. seconds ment. Corrections from figure ad- justment. Final seconds. // Cape Small Mount Pleasant Sabattus Mount Blue Mount Harris Azimuth Mark Saunders Humpback Mount Desert Isle au Haut Circle used in V positions. O 00 fK) 'OOO 32 27 39 '339 35 05 22 -195 72 13 02 -447 130 54 59 '344 131 32 49 '928 171 43 10-933 179 05 58- 378 20S 3 1 00 -500 241 oS 17 -507 // d=o-i3 0-19 o'i7 OT2 OM I 0'l6 O '12 o-i8 O'll o '19 // // 00 TJO +0-0I0 39 '35 -o'39 39 74 +0 -003 22 '20 -0-27 21 -93 —0 -049 02 -40 -4-0 -I I 02 -5 1 -ooo 59 '34 —0 -20 59"'4 +0 -025 58 -4" Q-OO 58-40 +0-OII 00-51 +0-04 00-55 Afount Blue, Franklin County, Maine. August 29 to November 5, 1S53. 75 ^ airection theodolite No. I. A. D. Bache and G. W. Dean, observers. Peaked Mountain 00 00 -ooo ±0-14 00 -00 Saunders 7 35 33 784 0-17 16 Mount Harris 8 46 42 -896 o-iS —0-003 42-89 -024 42-65 17 Ragged Mountain 35 42 23 70S 0-16 — 0-019 23 '69 4-0-15 23 '84 Cape Small 74 II 02 -283 0-20 18 Sabattus 76 57 34 '640 0-15 — o-oo8 34-63 +0-15 3478 19 Mount Independence 94 02 02 -93S 0-30 -000 02-94 —0 -20 02-74 20 Mount Pleasant 121 17 49-712 0-15 +0 -027 49 74 +0-03 49 77 Circle used in IV positions. Sabattu^, Androscoggin County. Maine. June 18 to Attgust 16, 1853. 75 ^■" clirection theodolite A. D. Bache, C. O. Boutelle, J. E. Hilgard, and G. \V. Dean, observers. 23 24 25 21 22 Mount Blue Azimuth Mark Mount Harris Ragged Mountain Cape Small Mount Independence Mount Pleasant o 00 00 -000 17 56 05 -204 69 29 07 -402 loi 37 20 -637 172 59 00-194 222 21 04-15S 275 46 51 '399 ±0 -II o -17 o -18 0-17 o -14 0-13 0-14 -o -032 59-97 -+-0 -021 +0 -005 07-42 20 -64 4-0-007 ^ o -1)14 04-16 51 -41 — 021 4-o-i6 -f 0-24 — o -07 — o -02 No. I. 59-76 07-58 20 -ss 04-09 51 -39 N. B. The observation of the direction to Mount Washington is too weak to be admissible. Circle used in IV positions. ii6 THE EASTERN OBLIQUE ARC. Abstracts of horizontal directions as observed and adjusted at the principal stations between the Epping base net, the Massachusetts base, and the Fire Island base net, /84^f-7882--continued. Mount Pleasant, Oxford Comity, Maine. July 2 to August 16, 1851. 75 "^"^ direction theodolite No. i. A. D. Baclie, W. P. Trowbridge, and G. W. Dean, observers. Number of directions. Objects observed. Resulting direc- tions from station adjust- ment. Approxi- mate prob- able errors. Reductions to sea level. Resulting seconds. Corrections from figure ad- justment. Final seconds. / // // // // // // 26 Mount Blue* 00 GO '000 drO-IO +0 -043 00 -04 — G -II 59~'93 27 Sabattus 51 26 46 -938 '12 -f -006 46-94 + 0-13 47 '07 28 Ragged Mountain 54 39 35 737 0'14 +0 -007 35 74 — -20 35 '54 Cape vSmall S3 01 37 -055 G -11 29 Mount Independence 100 12 48 -045 0-09 —0 'ooS 48 -04 -0-49 47 '55 Ossipee 146 17 24 '539 o-o8 30 Againenticiis 147 14 47 -657 G -14 — G -003 47 '65 + 0-77 48 -42 31 Gunstock 192 06 52 -382 '09 + '040 52-42 -G-23 52-19 34 Mount Washington 279 18 34-810 G -24 — G '102 3471 +0-38 35-09 Circle u.sed in V positions. Mount Independence, Cumberland County, Maine. September 2 to October 19, 1849. 75"" direction theodolite No. i. A. D. Bache and G. W. Dean, observers. 39 Mount Blue g 00 00 -ooo 44 36 -450 4G Sabattus 25 16 42-166 33 03 -048 51 14 '438 49 46 -990 37 Gunstock 253 42 01 -296 28 23 -886 N. B. — Observation of direction to Mount Washington too rough for use. Circle used in VI positions. Mount Washington, ■\ Coos County, Ne-w Hampshire. Station mark of 1851 and i860. 30^"' direction theodolite No. 118. July 31 to September 13, 1882. J. A. McNicol, observer (R. D. Cutts, chief of party). ^-^' ^ , 1 1 It It It 1 1 t f Mount Blue G Azimuth Mark Sabattus 25 Cape Small > 87 Agamenticus 207 Ossipee 241 Gunstock 253 Mount Pleasant 307 ±G-I4 — -002 OG -GO +0-36 00 36 -16 15 -fo -QIC 42 -18 -|-o -02 42 20 -16 G-I7 -f G -010 14-45 — 0-3G 14 ■15 -20 -20 + -023 01 -32 —0-60 00 -72 0-13 -G -G33 23-S5 +0-29 24 -14 Reference Mark G OG GO -GO ±0-07 33 Mount Blue 46 31 41 -34 -II + G -02 41 -36 -G-I3 41 -23 34 Mount Pleasant 115 27 23 -90 G-13 — 0-03 23-87 —0 -16 23-71 35 Gunstock 174 08 45-65 -14 O-QO 45-65 -fO-30 45-95 Killington 229 44 57-67 G-I7 Mount Mansfield 274 iS 19 -g8 0-I4 Circle u.sed in VII positions. * .\7.imuth mark west of Mount Blue 2"-i9 ± o"-ii. tThis station was established in September, 1849, by T. McDonnell at the highest part of the mountain. It was marked by a copper bolt inserted in a bowlder by G. A. Fairfield in 1851, and re-marked in 1853 by B. F. West. The pole placed over the mark was observed upon from Mount Independence in 1849, from Ossipee in 1851, and from Sabattus in 1853, but only roughly. The observations from Mount Pleasant in 1851 and from Gunstock in i860, however, were quite satisfactory. In 1877 C. H. Sinclair vLsited the station and under the direction of Assistant R. D. Cutts connected geodetically the several eccentric station marks since 1873 and again, in iSSo and 1881, those used by Prof. E. T. Quimby in his survey of the State of New Hampshire. These last obser\'ations have no bearing on the oblique arc, the only direction in common being that to Sabattus. Between July 31 and September 13, 1.S82, Assistant Cutts and Aid J. A. McNicol observed horizontal angles at the station in connection with the survey of New Hampshire, b\it included the three directions to Mount Blue, Gunstock. and Mount Pleasant. The 30':") theodolite was then employed. THE MAIN TRIANGULATION. 117 Abstracts of horizonlal directions as ol>scri>e(l and adjusted at tlic principat stations between the I-,ppinjr base net, the Massachusetts base, and the Fire /stand ttase net, /ut only in connection with the .sur\-ey of New Hampshire: it was reoccupied in September. 1S97, bj- As.sistant .\. T. Mosraan, in connection with western work in Vermont. fThe station was occupied by I'rof. E. T. Ouimby in July, 187-'. in connection with the s>ir\ey of New Hampshire. He used 25'-i" theodolite No. 31. He sighted Monadnock. and Patuccawa, but for these obsereations w-e have no use here iiS THE EASTERN OBLIQUE ARC. Ahslracts of horizon /a! directions as obscri'ed and adjusted at the principal stations between the Epping base net, the 3lassachiisetts base, and the Fire Island base net, /S-/^-/SS2 — continned. Thompson, Essex County, Massachusetts. October 15 to November 24, 1S46, and July 27 to August 23, 1847. 75"^"' direction theodolite No. i. A. D. Bache, observer. iber of ctions. objects observ ed. Resulting direc- ,^ ;. Reductions to sea level. Resulting seconds. Corrections from figure ad- justment. Final seconds. / // // // // // // 73 Manoniet 00 00 ■QOO rfcO-l8 —0 '002 GO '00 -fo'IO GO •JO 74 Blue Hill 44 15 19752 O'll 4-0 ■Oil 1976 + 0-I4 19-90 75 Wachusett Holt 90 104 52 48 38 782 53 '491 0-I2 0-13 + 0-0I0 38 -79 '00 38 -79 76 Unkonoonuc Patuccawa 129 154 22 45 49 757 22 -283 •14 '12 — -021 49-74 +0 -11 49-85 77 Gunstock 161 29 50 -943 0-I5 -0 -035 50-91 -0-23 50-68 Aziijuith Mark, west 1.S6 35 38 -458 '19 .... Aziinuth Mark east 190 40 47 -449 0-29 78 Aganienticus Isle of Shoals 191 201 13 26 43 -021 34-383 '12 'II + '001 43-02 — o'i4 42-88 Circle used in III positions in 1S46. JVachnsett, Worcester County, Massachusetts. September 13 to October 16, i860. 75'='" direction theodolite No. i. A. D. Bache and G. W. Dean, observers. Azimuth Mark 00 GO 'OOG =bo-io 65 Bald Hill iS 32 53-177 -20 66 Mount Tom 60 52 05 -024 0-34 67 Monadnock 150 38 43 -050 0-13 68 Gunstock 194 20 24 -085 G '14 69 Unkonoonuc 198 09 22 750 0-13 Patuccawa 212 49 54 -036 '12 Holt 249 13 40 -236 0-15 70 Thompson 255 42 43 -548 0-I7 71 Blue Hill 2S9 46 57 -469 0-13 72 Beaconpole 320 47 46 -S73 0-I2 +0 '017 +0 -016 — G '042 +0 '027 + G -018 OG 'OO 53-19 05-04 43 -oi 24 'ii 22 77 4-0 '00 1 — o '009 — o '009 43 -55 57-46 46 -86 +0-G7 -I -17 -fo-23 40-13 — o -07 -0-05 'O -G2 -0-15 Circle used in V positions. 53-26 03-87 43-24 24-24 22 -70 43-50 57-44 47-01 Blue Hill, Norfolk County, Massachusetts. September 14 to October 19, 1845. 75'^"' direction theodolite No. i. A. D. Bache, observer. 79 Manoniet So Copecut 81 Great Meadow 82 Beaconpole 83 ■Wachusett 84 Unkonoonuc Holt Azimuth Mark 85 Thompson 00 // GO -GOG // ±0-11 // —0-007 // // +G-I4 // 59-99 00-13 49 17 23-167 0-14 —0 -ooi 23-17 -40-03 23-20 67 01 11-778 G-II -fO -G02 II -78 —0 -OI II -77 103 II 18-606 -14 40-010 18-62 -0-52 18-10 170 05 20 -382 G -12 — -028 20-35 -t-0-20 20-55 209 46 13 -547 0-13 —0-018 13-53 -fo-23 13-76 234 48 06-131 G -10 .... 236 05 03 -497 G -09 269 23 57 -425 o-io 4-0-005 57-43 —0-07 57-36 Circle used in ^VI positions. THK MAIN TRIANGULATION. 119 Abs/rads 0/ liorirjoiita/ directions as observed and adjusted at the principal stations between the Epping base net, the Afassachnsctts base, and the Fire Island base net, 1844-/882 — continued. Great Meadow, Bristol County, Massachusetts. May 7 to 27, 1S45. 75*^'" direction theodolite No. i. A. D. Bache, observer. Resultiiif! direc- Ar,r.rr,vi Corroctioii.s Number of ,.k;..„*.. „k„<.„.<.^ tious from „r,te nrolV Keductions Resulting f directions. Objects observed. stati^i adjust- ^„^,^ ^.^^^^ .,^....^i.«..., .^^.,. J, .roni Final to sea level, seconds. figure ad- seconds, justment. 104 101 102 103 Copecut Beaconpole Massachusetts North Base Blue Hill o 00 00 'oaj 160 29 59 'SSI 219 19 14-351 229 39 39 'oSo ±0 '14 0-15 o 19 o '14 — O TX36 — o '009 o "000 +0 -005 59 '99 59 '34 14-35 39. oS -o -28 +0 -28 — o -24 -t-o -20 59'7i 59-62 14-11 39 ■2.S Circle used in III positions. Copecut, Bri.stol County, Massachu.setts. September 7 to October 8, 1844. 75'" No. I. A. D. Bache, oh.server. direction theodolite 92 Blue Hill and Azi- / // // // // // // inuth Mark GO 00 '000 ±0-13 —0 '002 00 -oo —0-19 59 -Si 93 Manoniet 64 oS 37-851 -16 +0 '006 37 -86 -rO-QI 37-87 Indian 140 03 44 -563 0-15 90 Beaconpole 318 01 oS -556 0-13 — Q-OIO oS-55 -0-17 08-38 91 Great Meadow 328 04 06 -825 0-15 —0-005 06 -82 +0-39 07 -21 Circle used in III positions. Manoniet, Plymouth County, Massachusetts. August 25 to September 11, 1845. 75'^'" direction theodolite No. i. A. U. Bache, observer. Provincetown 00 00 -ooo d=o -11 Indian 120 13 21 -474 'ID 86 Copecut 172 29 05 -212 0-T7 87 Beaconj.ole 209 03 27 '009 -16 88 Blue Hill 239 03 09 -898 -10 89 Thompson 284 II 54 '745 0-13 Circle used in VI positions. -fo -006 — o. 002 — o -on — o -001 05 -22 27 01 09 89 54-74 Massachusetts South Base, Bristol County, Massachusetts. September 9 to theodolite No. 11. E. Blunt, observer. +0-07 +0-I0 — o -08 — o -06 05-29 27-11 09 Si 54-68 1845- 25 '"' repeat ins^ 105 Beaconpole 00 00 -cx^ 106 Massachusetts North Base 81 00 16-66 0-45 (-0-004 59 "99 16-66 3/assachusetts North Base, Bristol County, Massachusetts. September 19 to 29, 1S45 theodolite No. 11. E. Blunt, observer. — o -20 -f o -20 !5 59 79 16 -89 repeating 107 Great Meadow 00 cx)-ooo =to -35 -ooo 00 -oo -fo-26 00 -26 108 INIassachusetts South Base 25 16 31 -173 -35 +0 -002 31 -iS — 009 31 -09 109 Beaconpole 70 09 29 -s 1 2 -35 ro -006 29 82 -0-I7 29 -65 I20 THE EASTERN OBLIQUE ARC. .-Ibstracts of horizontal diirctions as observed and adjusted at the principal stations hetiveen the Eppitis; base net, the Massachusetts base, and the Fire /stand base net, /iV^^-z^^i"— continued. Beaconpole, Providence County, Rhode Island. October 19 to November 23, 1844. 75 "" direction theodolite No. i. A. D. Bache, observer. Number of directions. Objects observed. Resulting direc- tions from station adjust- ment. Appro.Ki mate prob- able errors. Reductions to sea level. Resulting seconds. Corrections from figure ad- justment. Final seconds. Wachusett f 00 // GQ-OOO // d=0 '11 // -0 -034 f f // —0 -26 " 94 59 '97 5971 Azimuth Mark 35 12 22 -656 o-i6 95 Blue Hill 82 05 13 "35' O'll + 0-0I2 13 -36 +0-40 1376 96 Massachusetts North Base 105 44 12 '597 0-15 -f -002 12 '60 +0-17 12-77 97 Maiiomet 1 28 54 18-252 -16 — "001 18-25 -0-28 17-97 98 Great Meadow 156 45 30 -025 0-09 —0 -005 30-02 -0-I5 29. 87 99 Massachusetts South Base 159 50 57 •«43 TI — '002 57-84 —0-03 57 -'^i 100 Copecut 166 12 31 431 o-io — o"oo6 31 -42 +0-13 31 -55 Circle used in IH positions. JMonadnoc/c;* Cheshire County, New Hamp.shire. July 21 to August 15, r86i. 75* direction theod- 60 Gunstock 61 Unkonoonuc 62 Wachusett 63 Bald Hill 64 Mount Tom olite No. . G. W. Dean, observer. / 00 // GO -QGO ±0 -lo // -f -042 // 00-04 ~o-i4 /' 59 '90 32 54 52 '457 -19 -f -G14 52-47 O-GO 52-47 117 01 19-427 -10 —0 -026 19 -40 — G-I2 19 -.-28 145 06 44-724 -09 +0 -004 44 73 + -35 45 -08 173 46 06 -97 1 -ir 4-0 -019 06 -99 — -08 g6 -91 nervation ( D. and A' ) of a direction, er- = ±0^.67. Circle used in V positions. Mount Tom,]- Tolland County, Connecticut. July 11 to August 16, 1862. 75"" direction theodolite No. I. G. W. Dean and R. ¥^. Halter, observers. OG OG -000 45 13 -052 28 4G -690 52 53 -979 18 15 -047 163 34 58 -584 Circle used in V positions. Batd Hill, ToUaiid County, Connecticut. September 12 to 25, 1861, and May 22 to June 7, 1S64. y-cm direction theodolite No. i. G. W. Dean, olxserver. 115 Monadnock Azituuth Mark 4 TI6 ■Wachu-sett 33 117 Bald Hill 95 118 Box Hill 129 119 Sandford 163 zhO -10 J-G -052 GO -05 -f 0-12 00-17 0-08 -09 + -G27 40. 72 +0 -30 41 -02 o'oS -0 -023 53 -96 -00 53-96 -09 — -009 15 -04 -0-13 14-91 -12 + -009 58-59 -0-33 58-26 no Box Hill G 00 OG -GOG ±o-g8 -f 0-015 00 -02 + 0-21 00-23 III Ivy 34 47 46 -780 -12 +0-0G7 46-79 -fo-28 47-07 112 Mount Tom So 50 44 -995 G 'IG ~o -022 44-97 —0-05 44-92 '13 Monadnock 136 18 39 -740 0-I4 + G -G09 39-75 — o-6i 39-14 114 Wachirsett 156 07 28 -560 -12 + -G2S 28-59 -+-0 '11 28-70 Circle used in "V positions in 1 86 1 and 1864. ♦This station was occupied by Prof. E. T. Quimby in June, 1872, in connection with the survey of New Hampshire. In September, 1878, the party of Assistant R. D. Cutts reoccupied the station, but neither of these observers made any additions to the measures of the oblique arc. t This station wasoccupied in June and July, 1877, by .\ssistant R. D. Cutts in connection with the survey of Vermont. THE MAIN TRIANGULATION. 121 Abstracts of horizontal directions as nt)scrvc(l aiict adjusted at the principal stations between the Eppiu)( base net, the Alassachusetts base, and the Fire Island base net, /H^-f-/8H2 — continuerl. Box Hill, Tolland County, Connecticut. Octolier 9 to 2.S, 1861. G. W. Dean, observer. 75"" direction theodolite No. i. Number of directions. Objects ob.served. Sandford Ivy Mount Tom Bald Hill Circle used in V positions. 120 121 122 123 Resulting direc- tions from statiiiii adjust- ment. O 00 00 "000 49 35 39'««i 114 15 55751 179 59 54 '087 Ajjproxi- mate prolj- al>lccrrors. Reductions to sea level. Resulting .seconds. Corrections from figure ad- justment. Final seconds. // // // // // ±0-13 -t-o-oi7 CX3 '02 -fO TO 00'12 -1 I —0 -007 39 '^7 -o-o8 39 78 'II -0-013 55 74 -^028 56 02 10 +0 -024 54 1 1 — 0-2S 53 •-'^3 Ivy, Litchfield County, Connecticut. June 29 to August 12, 1863. 75 "' direction theodolite No. i. G. W. Dean, observer. 124 Bald Hill 125 Box Hill 126 Sandford 127 Wooster O 00 00 '000 rbO 'oS +0 '007 14 48 02 '805 0'09 — o '004 71 09 55 '842 0-09 —0-013 118 50 47-463 0-I2 -I-0-0I2 Circle used in V positions. 00 -or —0-04 59 97 02 -So -0-13 02 -67 55-83 — -12 55 71 47 -48 -o'33 47 -81 Sandford, New Haven County, Connecticut. vSepteinber 9 to November 4, 1S62. 75^'" direction theo- dolite No. I. G. W. Dean, observer. Number of direc- tions. Objects observed. Resulting directions from station adjust- ment. Approx- imate probable error. Reduc- tion to sea level Correct- ed direc- tions. Correc- tions from net adjust- ment. Result- ing direc- tions. Correc- tions from fig- ure ad- justment. Final seconds. Ruland 00 OO'OOO ±o-ti —0-264 59-74 West Hills* 23 24 4! '547 -f -ooS 0-12 -1-0 -482 42-04 Tashua 42 36 58-413 0-12 -Ho -01 1 5S -424 -0 -330 5^-09 Wooster 69 03 33'ii3 0-24 -(-0 -009 33-122 +0 -356 33-4S Azimuth Mark 85 20 30. 246 0-15 128 Ivy 147 34 47 -646 0-15 —0 '024 47-62 -1-0 -25 47-57 129 Mount Tom 190 09 54 '5^1 0-12 -1-0 -012 54 59 -l-o-ii 5470 130 Box Hill 22: 37 22-062 O'lO -1-0 -016 22 -oS -1-0 02 22-10 Circle used in V positions. Wooster, Fairfield County, Connecticut. July 14 to October 10, 1S64. 75" G. W. Dean, observer. direction theodolite No. i. 131 Ivy 00 00 -000 ±0-07 Sandford 53 47 59-20S -07 Tashua 95 57 47 652 o-oS Ruland 124 51 45 -93S o'oS West Hills* 154 10 3S -493 +0-032 0-07 Circle used in V positions. -f -020 00 -02 -1-0 -009 59 '217 -o_o69 59-15 -0-009 47643 +0-285 47-93 +0 005 45-94 -0-147 38-3^ *The correction to direction of West Hills Is for eccentricity. —0-29 59 122 THE EASTERN OBLIQUE ARC. Observation equations. I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII = o= o= = o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= o= — o -45- +o -46- -o -38- +0 -09- -o -08 - -o -66- +0 -49- +0-07- (i) + (2) + (i) + (7) + (7) + (8) + (4)- (2)- (9)- (8)- (9)^ ;i4)+ (5)+ (6) + :i2)+ ,15) (6) (7)- :r3)- (io)+ (12)- (i8)+ {20)- +0-85- (21)+ (22)- +0-09- (19)+ {20)- -] -42- (31)+ (32)- + I-20- {36)+ (37)- -2 ■02- (29)+ (30)- + 1 -22- (30)-f- (31)- + 0-39- (44)+ (45)- (ii)+ (13)- {i6)+ (18)- (17)+ (20)- (22)+ (23)- (27)+ (29)- (26)+ (29)- (34)+ (35)- (41 (43)+ (44)- (51 (49) (45) (55) (45) + 1 -05- +0-03- — o '27 +0-6I- —0-23- (46)- +0-6I- (57)- +0-69 - +0 -37- -I '55- —0-25 — — o '62— +0 -84- +0-07- + 1 -lo— (36)+ (42)+ (49) + (54) + (55)- (69) + (50)- (46) + (57)- (47)- (48)- (58)- (55)+ (56)- (70)^ (71)- (71)+ (72)- (73)+ (74) + (86)+ (87)- (80)+ (82)- (79)+ (80)- (86)+ (88)-^ (80)+ (81)- (91)+ (92)-- -I -41- (90)+ (9i)~ (98) + (ioo) + + 1-28- (96)+ (98)-(ioi) + (io2)- -oTi- (96)+ (99)-(io5) + (io6)- -1-62- (62)+ (64)- (66)+ (67)- + I-IO- (63)+ (64)-(ii2) + (ii3)- + 1-37- (65) + +o'96— ( iio) + +0 '22- (lI0) + +0-II— (ii8) + +0-41 — (120) + —0-99— (126) + (66)- (112)- (III)- (119)- (121)- (127)- -(II2) + (II4)- -(ii7) + (ii8)- -(I2l)+^I23)- - (120)+ (122) — -(I25) + (I26)- -(i28)-(i3i) (13 (16 (24 (23 (26 (26 (38 (38 (38)- (52 (44)-- (51 (51)- (77 (76 (76 (75 (75 (60 (67 (84 (83 (94 (88 (97 (55)-- (59)- (70)- (68)+ (70)- (58)+ (59)- (6i)+ (62)- (74)+ (76)- (74)+ (75)- (82)+ (83)- (79)- (85)- (90)+ (93)-- (90)+ (92)- (95 (92 (103 ( lOI ( 107 (108 (115 ("5 (116 ( 122 (124 ( 129 (128 + (15) + (17) + (25) + (24) + (28) + (27) + (40) + (39) + (42) + (53) + (53) + (52) + (78) + (78) + (77) + (76) + (77) + (61) H- (69) + (85) + (85) + (95) + (89) 100) 100) (93) 104) 104) 109) 109) 116) 117) 117) 123) 125) 130) 130) + -3'8-2-77(i)+3"39(2)+4-29(3)-3'35(4) -i •43( i3) + i •89(14) -o -46(15) -I 7+o-2i(ii) + i -28(12) — I •49(i3)-3-3o(i6)+4-i4(i7)—o-84(i8)-o -79(23) +4 -14(24) -3 '35(25) THE MAIN TRIANGULATION. Observation ftjucUioiis — coniiiiue'l. 123 I XLIII o= — 1 +0 XLIV o=— +4 XLV 0= J I XLVI — 1 o=~6 + 3 XLVII o=-|-o + 3 XLVIII o= — I — XLIX o= — I +3 Iv 0= + 2 + 1 LI o=— +5 WI o= — 2 + 2 LIII o=— — IvIV o= + i + 4 LV o= — I +7 LVI o=+5 + 2 +2 — I — +0 + 1 — I —0 +0 LVII 0=+2 — 2 — 2 + +0 -3 + 1 •S2J-4 •5S6( 10) -4-864(11) fo -278(12)^0 •2401 17)— =o-8 =0-9 =0-9 =0-9 =o-8 = i'i = l'o =o-8 =0-9 =0-9 = i"o =0-91 = I"Oi =o-8 =o-8 = i-o = I'0' =o-8 =o-8 =o-8 = i-oi = I'2 =0-9 =0-91 =3-8i =3-8 =2-51 = 2-5' = 2-5 =o7' =0-9 =o-8' =0-9 =0-9 =o-8 =o-8 =07 =o-S =0-9 =0-9 +C=g-t-o-947C53-2-SSC56+2-88C5 —C,4-!-C2-— 2-0305 -2-S8C55J-2-SSC56-2-88C5 -C.,+a4-2-54C5,) -C22^I-24C56+2-54C57) ^C,,+ C,5-C=5-I-24C56) -C.6-C.8~2-84C5.) +C.6-3-65C5x+6-49C5=) -C.5+C.3^574C5,-3-65C5=) ^C^;- 2 -0905.) — C^e -C^j — Cj:,— 2-95052— I • ISSC53) +C=,~C.8+C.5+2-34C5.-o-338C33) + C.6 + C38+0-6IC5.) — C.4 — 0-2905, +0-29C56—0-29C57) + C\4-C,, + 2-27C5,-0-058C5,-0-29C5<;+0-29C5,; -C\,-C3.-r52C56^r52C5,) — C26— i"98C5,) -C30+C3. + 1-323C53) +03,-1-1-52056— 1-52057) + C.6-f-C.,-^03o-I-265053) + 03c,-03x-O-480s6+O-48057) +03,-1- 1 -28056-1-2805;) — 029— 0-80056+0-S0057 ) +C.5-030) — C30+0-33056— O-33057 ) +03=-o-33056+o-33057) -03,+o-76056-o-7605,) -C3.) + 03,+03.-o-76056+o-7605, ) -0,6-03,-2-69055-0-3405;) + 037^3-03055) -0,4-035+036-o-55C54-o-3405s+o-8905;) +034+5-84054) + C35-5'29C54-o-55C57) -033-034-3-18054+3-1805;) +033-035+4-28054-3-1805;) +034+035-0,6-1-10054-3-19055) +036-038+6-28055-3-0905;) + 0,8- 3-O9O55 + 3-O9O57) -C38-C35-I-79C5;) THR MAIN TRIANGULATIOX. 12" -:& Conrlalc equal ioiis — coiiij)lelc-(l. .2 o V. 5.1UJ '0 3J V > (121) =o-8( (122) =o-8( (123) =o-8( (124) =07 ( (125) =o-8( (126) =o-8( (127) =o-9( (128) = i-o( (129) =o-9( (130) =o-8( (131) =o7( -C37+C„+r79C57) -C36 + C38 + 0-95C57) +036+037-0-95057) -C37 + 7-97C55) +0,7-035-9-37055- 1-40057) +035-040+1-40055-3-32057) +040+1-92057) -035+040+0-60055) -038-3'44C55+3-44C57) +038+035+2-84055-3-44057) -040-f I-54C57) Normal eqiialions. Ci C2 C3 C4 C5 C6 C7 C8 C9 Ci3 Cii Ct2 Cn C.4 C.s I o=-o-45 +3-6 + 1-6 2 0= +0 -46 +3-6 -i'7 3 o=-o-38 +4-9 -1-6 -1-6 4 o=+o -09 +5-5 + 1-6 + 2-0 -1-9 5 o=-o-o8 + 5-8 — 2 -O 6 o=— 0-66 +5-8 — I -S 7 o=+o-49 +5-8 + 1 8 4-l-S 8 o=+o-07 + 5-4 -I -8 + 1-8 9 0=4-0-85 +5-4 + 1-7 —1-7 10 o=+o-09 +6-4 -t-7 II o= — I -42 +5-7 -1-6 12 0=i-I -20 +5-9 + 2-0 4-1 -8 -I -s 13 0=— 2 -02 + 5-5 — I '8 14 0= + I '22 -**5 - -fS Normal equations— -continued. C.5 C,6 C.7 C18 C15 C20 C2, C22 C=3 C24 C25 C25 C27 C28 C2, C3, C„ C32 C3J 15 o = +o'39 -t-5-5 4-1-8 -1-9 -rg 16 0= -f I -05 -t-5-5 -I-I-7 -1-7 -17 17 0=4-0 -03 -I-5-0 -1-7 4-1-9 -1-4 - ■'7 18 o=— o'27 -(-5-3 4-2-0 -1-6 4-1-7 -2-0 19 o=+o-6i -I-5-6 — 2-0 20 o=-o-23 0= -1-0 -61 4-l-s —1-6 21 .... -ri| J I Kj -I-4-9 22 o=+o-69 4-5-2 4-1-6 -1-6 ~ ' 23 o=+o-37 -1-5-4 -i-S -1-6 24 o=-i-55 4-5-2 -1-7 25 26 o=-o-25 o=— 0-62 4-5-2 ~\'^ 4-5-8 4-1-7 4-2-t + 1-7 27 o=+o-84 4-5-2 -1-8 4-i-S 4-1-7 28 o=+o-o7 +5-5 — rS 29 0=4-1-10 +5-4 -1-9 30 o= — I -41 -t-5-4 -1-8 +9-0 4- 5'5 31 0=4-1-28 32 o=— o-ii + 144 128 THE EASTERN OBLIQUE ARC. 0= — I ■ o= + i- o= + i- 0=+0' o=+o ■ 0=+0' 0=+0', 0=— 0'' o=-3-: o=-i • o=-i ■; 0=— O'i o= + i ■■ o=-6-: Cjq Ci4 Nonn.il t't] nations — continued. C36 C37 C38 C59 C40 C41 C4 C43 C44 C46 + 6-6 + 1 ■6 -3 ■3 +4 •8 + 1 •5 — I ■5 + 7 ■0 — I +4 ■5 •6 + i'5 +4 7 +5-1 -1-6 + 17 + 5-1 -1-8 +3-4 +51 '123 +1705 +64-821 + 0-573 +78-136 + 3-95 — II 'oo + 170 '86 + 1-36 - 77-26 + 3-004 + 185-75 -27 400 + 54-542 Norma/ equations — completed. C41 C4C C43 C44 C45 C46 C47 C4f C49 Csc C5. C5= C56 I +3-630 + 1 -848 2 -6 -736 -5-395 3 +6 -043 + 1 -192 +6-109 4 -I -144 +5 -426 -o-oio + 1-355 5 -I -144 — 9-662 +5 -350 -9-4S0 6 + 7-976 -0-455 - 4-700 + 3-929 7 - 2 -988 - 2 -037 - 0-806 + I-20S -t-o-So6 8 -ho -208 -2-990 + 7-071 + 1 -20S +0 -S80 9 +3 -526 - S-243 -2-835 — I -624 +3 -502 10 +o-o8i - 1 1 -558 +5 -084 - 1 -624 +0 -44S II -4 -225 -2-520 +2-520 12 +0 -462 -8 -218 -2-583 +6-604 13 + I -066 + 2-835 -2-228 + 2-458 14 -4-944 + 2-106 -2-583 -3-132 Normal (•(/«< - 27-64 + 4-307 -4-096 48 = — I ■23 + 36 •187 + 32 -60 — -853 + '93 + I -793 49 = -1 ■7 + 139-92 -10-125 + 9-33 + 0-450 + 9-489 + 0-892 50 = +2-4 +5S72S - 39-07 - I 472 + 3-767 51 = —0 ■7 + 135-18 —40-449 —0-106 - 32 -680 + 32-440 52 = -2 ■0 +S0-S20 +2-056 - 5 '261 + 5-261 53 = —0 ■61 + 7 -56S - 2-914 + 2-914 54 = + 1 •4 +9S -900 + 2-61 - 14 -99s 55 0= — I •0 + 194 -42 - 56-399 56 = +5 7 + 171 -07 - 52-148 57 0= + 2 ■6 + 74-110 C , =+0 -1207 C 2= — o -1272 C 3=— O -0699 C 4 = -o-32iS C5=+o-i829 C6=+o-33i8 C 7=— O -2663 C8=+0-I052 Cg=+o-i69S Cio=+o-2558 Ci, = +0-3849 C,.= -0-2855 C,3 = +o-6S2i C,4= +0-0849 C:5=--0-I424 Resultius:; values of correlates.. Ci6=— o -2409 C,./=+o-iSii C,i;= +0-4276 C,5=— 0-3196 Coo=-Lo -I91S 0=, = +0-1744 C=.= -0-3624 C23 = +0-I242 C,4 = +0-3096 C25=— O -0829 C,6=+o-2957 C.; = -0-1935 Cj8=— 0-2701 C;9=— o -1904 €30= C3.= ^32 ~ C33 = C34 = C35 = C36 = C37 = C38 = c„= C4a = C4.= C4= = C43 = :-rO-i223 ^-0-1395 = +0-0363 : +0-4168 = -0-5315 :— O -OI9I — o -6061 : — O -2410 :— O -2491 : -0-1599 = --0-3927 + -0652 :+0 -0481 : +0-0123 C44 = -0 -0449 ^45 = -0 -0375 C46 = -f-o-i3i5 C47 = — 0635 C48 = -rO 0569 C49= — 0056 C30 = -0-0143 C3,= -0 -0053 C5= = — 0325 C5.= -0 -0530 C54 = — -0247 C55 = — "0236 Cs6 = — 0590 ^57 = — 00136 A'esiil/nii;' corrections to directions. (i)= -0-054 (2) = +0-I03 (3) = -fo-36o (4)=-o-44i (5) = -o-oT4 (6)=:+o-o7o (7) = +o-o55 (8) = -o-oii (9) = -o-ii4 (10) = +0-387 4192 — No. 7 — 02- (34) = -o-i55 (35) = H 0-303 (36) = -0-304 (37) = --0-603 (38) = -1-0 -294 (39)=-^-o■356 ■(4o) = ^o -017 (41) = -0-401 (42) =-0-044 (43) = -f-o-8oi (67) =+0-228 (68) =+o-i26 (69) =-0-074 (70) = -0-049 (7i) = --o -oiS (72) = — 0-152 (73) = -o-io4 (74) = +o-i36 (75) =-0 -002 (76) = - o-no ]oo)=-ro -126 ioi)=— 0-284 102) = -0-237 103) = — 0-204 104) = — 0-281 105) = — 0-195 106)=— 0-195 107) =—0-262 ioS) = — 0-091 109) = — o -172 I30 THE EASTERN OBLIQUE ARC. Resulting corrections to directions — continued. (II)= — •270 (I2) = ^0 ■loS (13) = — ■199 (14) = + ■003 (15) = +0 •03S (i6) = — •240 (17) = +0 ■147 (iS) = +0 ■146 (19) = — •202 (20) = +0 ■027 (21) = — ^0 •070 (22) = — •025 (23) = ~o •212 (24) = -ho •■65 (25) = ^0 ■241 (26) = — •106 (27) = +0 •130 (2S) = — •19S (29) = — •4SS (30) = +0 •769 (31) = — •229 (32) = +0 •375 (33) = — 132 (44) = = — ■081 (45) = = — •198 (46) = = +0 ■104 (47) = = — •404 (48) = =+0 •154 (49) = =+0 •391 (50) = = — •321 (51) = = +0 ■025 (52) = = ~o ■'59 (53) = = +0 •006 (54) = = +0 ■112 (55) = = -f-0 •022 (56) = = — •347 (57) = =+0 ■155 (58) = = —0 ■034 (59) = =+0 •012 (60) = = --0 •139 (6i) = = — ■004 (62) = = — ■125 (63) = =+0 •347 (64) = = — ■080 (65) = =+0 •066 (66) = = — I •16S (77) (78) (79) (80) (Si) (82) (83) (84) (85) (86) (87) (88) (89) (90) (91) (92) (93) (94) (95) (96) (97) (98) (99) Proba])le error of a resulting direction =o"674 /8^ _ V 57 ~ = -0-231 = -0-139 = +0-137 = +0.-026 = — o-oo8 = -0-525 =+0-198 = +0 -229 = — o -066 = +0-073 = +0 -104 = -o -079 =—0-065 = — o -172 =+0-394 = — o -187 = +0 -006 =-0-257 = +0 -401 = +0 -172 =-0-285 =-0-153 = — o -026 ±:0"-26. (no) = J-o •214 (III) =+0 ■281 (112) = — ■050 (113) = — -60S (114) =+0 ■107 (115) =+0 -120 (116) =+0 -299 (117) =+0 -005 (iiS) = -0 •133 (119) = -0 •32S (120) =+0 -102 ( '21 ) = — •084 (122) = +0 ■275 ('23) = — -282 ('24) = ~o ■037 (125) = — -127 (126) = — •124 (127) =+0 •330 (128) =+0-247 (129) =+0 •109 (130) =+0 •020 (131) = — -290 Rt suiting angles and sides of the tri angulation between the Epp ing base net an (/ the IMassachnsetts base: also between this base and the Fire Island base net. vTo stations. Observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. Log. dis- tances. Distances in meters. / // // // // Ragged Mountain • Humpback Mount Desert 29 25 02 -II +0-04 02 -15 3-44 4-761 268 57 712-253 I 39 54 29 -08 + 0-36 29-44 3-44 4 -.^77 280 4 75 384 -2 2 no 40 38 -68 + 0-05 38 73 3-44 5-041 137 6 109 935 '4 Mount Harris 40 32 25 '22 +0 -08 25-30 3-79 4-761 268 57 7'2-253 2 • Hinnpback Mount Desert 66 02 38-5' -0-44 38-07 3 -80 4-909 249 6 81 142 -72 73 25 08 • 1 1 — TO 38 -or 3-79 4-929 927 85 099 -50 Mount Harris 65 08 2,T27 — -02 37-25 3-13 4 -877 280 4 75 384-21 3 Mount Desert 37 '5 30 '57 + 0-16 30-73 3-13 4 -701 544 4 50 297 -27 Ragged Mountain 77 36 o( -17 + -24 01 -41 i"^i 4-909 249 6 81 142-72 Mount Harris 105 41 02-49 -F -07 02 -56 3-49 5 -04' 137 6 109 935 -4 4 Humpback 26 08 09 '43 — o-8o 08-63 3-48 4 -70' 544 4 50 297 -27 Ragged Mountain 48 10 59 '06 +0 -20 59-26 3-48 4 -929 927 85 099-50 Mount P.lue 26 55 40 -So 40-39 41 -19 4 -02 4-701 544 4' 50 297 -27 5 IMount Harris 94 22 34 -42 - 0-17 34-25 4-03 5-044 318 I no 743-5 Ragged Mountain 58 41 56 94 -0-31 56 63 4 -02 4-977 267 I 94 900 -20 THE MAIN TRIANGULATION. 131 A'l-su/////,!,^ aitffh'x and sides of the Iriatiffulalion behveen the Eppinj:; base base; also betiucen this base and the Fire Island base net net and the Massachusetts — continued. No. 12 13 14 15 16 17 stations. observed angles. Correc- tion. Spher- ical angles. Spher- ical exce.ss. Log. dis- tances. Distances in meters. / // // // // Sabattus 32 08 13 -22 +0 -08 13 -30 3-15 4 -701 544 4 50 297 27 Mount Harri.s 52 02 19 -02 —0-07 18 -95 3-'5 4-872 442 9 74 549 ■19 Ragg;pd Mountain 95 49 37 '14 + -07 37-21 3-i6 4-973 438 4 94 067 -25 vSabattus 69 29 07 -45 +0 -38 07 -83 5 -09 4-977 267 1 94 90f) •2f) Mount Blue 6S 10 5 1 74 + -38 52-12 5-08 4-973 438 4 94 067 25 Mount Harris 42 20 15 '40 —0 -lo 15-3" 5 -08 4 -834 048 9 68 241 -56 Sabattus lOI 37 20 '67 +0-45 21 12 4-22 5-044 3'8 I no 743-5 Mount Blue 41 15 10-94 'OO 10-94 4-21 4-872 443 74 549 -20 Ragged Mountain 37 07 40 -20 +0 -38 40-58 4-21 4-834 048 8 68 24' -55 Mount Pleasant 54 39 35 70 —0 -09 35-61 8-II 5-044 318 1 no 743 5 Mount Blue 85 35 26-05 — -12 25-93 8-IO 5-131 493 6 135 361 -0 Ragged Mountain 39 45 23 '05 — -28 22-77 8 -10 4-938 618 6 86 819-76 Mount Pleasant 51 26 46 -90 + 0-24 47-14 3-50 4-834 048 9 68 241 -56 Mount Blue 44 20 15 -II — 12 14-99 3-50 4 -785 231 60 986 - 1 2 Sabattus 84 13 08-56 — -19 08 -37 3 '50 4-938 61S 6 86 819 -76 Mount Pleasant 3 12 48 -So -0-327 48 -473 0-391 4 -872 443 f) 74 549 -20 Sabattus 174 09 30-77 -0-265 30-505 0-392 5-131 493 6 '35 361 -0 Ragged Mountain 2 37 42-85 -0 -654 42-196 0-391 4 -785 23' 60 986 ■ 1 2 Mount Independence 77 48 18 -a — -28 iS-05 1-94 4-785 23' 60 986 -12 Mount Pleasant 48 46 01 TO —0-62 00-48 1-94 4-671 377 7 46 922-13 Sabattus 53 25 47 '25 + -05 47-30 I -95 4-699 925 8 50 no -16 Mount Independence 25 16 42-18 -0-34 41 -84 1-83 4 -834 04S 9 68 241 -56 Mount Blue 17 04 28-31 -0 -35 ^ 27-96 1-82 4-671 377 7 46 922 13 Sabattus 137 38 55 -81 —0-14 55 -67 I -82 5-032 067 2 107 663-2 Mount Independence 52 31 36 -'5 -\- -06 36-21 3-62 4 -938 6:8 6 86 819-76 Mount Pleasant 100 12 48 -00 -0-38 47-62 3-62 5 -032 067 2 107 663-2 Mount Blue 27 15 46-80 + 0-23 47-03 3-62 4-699 925 8 50 no-i6 Mount Washington 68 55 42-51 —0 -02 42-49 3 '41 4 -938 618 6 86 819 -76 Mount Blue 30 23 02 -89 3-41 4-672 640 4 46 950 -53 Mount Pleasant 80 41 25 '33 -0 -48 24 -85 3 -41 4-962 918 5 91 S16 -03 Gunstock 34 '9 40 ■ 20 -1-0 -84 41 -04 3 -03 4-699 925 S 50 1 10 -16 Mount Pleasant 19 54 04 • 38 + -26 04 -64 3-04 4 -94S 470 6 88 Sn -79 Mount Independence 53 46 22 -53 +0 -90 23 -43 3 -04 4 -855 408 I 71 68 r -66 Mount Washington 58 41 21-78 +0-46 22 -24 2-85 4 -855 40S I 71 681 -66 Mount Pleasant 87 1 1 42-29 +o-6o 42-89 2-84 4 -923 248 I 83 800-79 Gunstock 34 07 03 -05 +0 -36 03-41 2-85 4 -672 640 4 46 950 -53 THE EASTERN OBLIQUE ARC. iS ^9 24 25 26 27 28 29 ///«!,'■ (DiQ'/t's aud sides of the triaiii^ulaiioii bctivccn the Epp i/ig' base net anc / the IMassaeluisetts base; also betzcech tliK ' base am / /he Fire Island base net— -continued. stations. Observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. Log. dis- tances. - Distances in meters. / // // // // Againenticus 85 39 41 '30 — 0-02 41 -28 3-59 4-948 470 6 88 811 -79 Gunstock 48 29 43 -Si -0-8S 42-93 3-59 4 -824 135 1 66 701 -43 Mount Independence 45 50 46 -87 -0-30 46-57 3-60 4 -805 515 8 63 902 -20 Aganienticus 33 20 57 -33 + 0-16 57-49 2-78 4-699 925 8 50 1 10 -16 Mount Pleasant 47 01 59 "61 + 1 -26 00 -87 2-79 4 -824 135 I 66 701 43 ]Mount Independence 99 37 09-40 + -60 10 -00 2-79 4-953 627 I 89 872 -56 Aganienticus 52 18 43 '97 — -18 43-79 3-84 4 -855 408 I 71 68 1 -66 Gunstock 82 49 24 '01 —0 -04 23-97 3-85 4 -953 627 89 S72 -54 jMount Pleasant 44 52 0477 — I -00 03 -77 3-84 4 -S05 515 8 63 902 -20 Unkonoonuc 53 00 53 '60 + -10 53-70 3-25 4-805 515 8 63 902 -20 Gunstock 76 II 25-06 + 0-19 25 -25 3-25 4 -890 346 8 77 686 -72 Agamenticus 50 47 50-46 + 0-35 50-81 3-26 4-792 336 4 61 992-11 Thompson 29 43 52-11 + 0-09 52 -20 3-23 4 -805 515 8 63 902 -20 Gunstock 31 52 27 -68 —0 -12 27-56 3-23 4 -832 776 9 68 041 -97 Agamenticus iiS 2 T 50 -30 -0 -36 49-94 3-24 5-054 430 8 113 352 -4 Thompson 61 50 53 -28 -0-25 53-03 4-13 4 -890 346 8 77 686-72 Unkonoonuc 50 33 20-33 — -09 20 -24 4-13 4 -832 776 9 68 041 -97 Agamenticus 67 35 59 '84 -0-71 59-13 4-14 4-910 955 Si 461 -99 Unkonoonuc 103 34 13-93 -fo -01 13-94 4-15 5-054 430 8 113 352 -4 Gunstock 44 18 57 -38 -1-0-30 57-68 4-15 4-910 955 I 81 462 -00 Thompson 32 07 01 -17 ~o -34 00-83 4-15 4-792 336 5 61 992 -13 Monadnock 32 54 52-43 4-0-13 52-56 I -93 4-792 336 4 61 992-11 Gunstock 22 59 06 -42 +0 -05 06-47 I -93 4-648 835 I 44 54S-71 Unkonoonuc 124 06 06 -72 +0 -05 06-77 ;-94 4-975 287 4 94 468 -59 Wachusett 61 22 19-44 -0-17 19-27 8 -68 5-054 430 8 113 352 -4 Gunstock 48 00 55-09 —0 -21 54 -88 8-68 4-982 231 4 95 991 -20 Thompson 70 37 12 -12 -0-23 II -89 8-68 5-085 731 5 121 S23 -6 Wachusett 57 33 20 -78 + 0-03 20-81 4-12 4 -910 955 81 461 -99 Unkonoonuc 83 56 40-35 + 0-13 40 -48 4-11 4-982 231 3 95 991 -18 Thompson 38 30 10-95 H-Q-Il 11 -06 4-12 4 -778 830 2 60 093 -88 Wachusett 3 48 58 -66 —0 -202 58 -458 -412 4-792 336 4 61 992-11 Gunstock 3 41 57-71 -0-510 57 -200 -412 4-778 830 3 60 093 -89 Unkonoonuc 172 29 05-72 —0 -142 04 -578 -412 5 -085 731 4 121 823-6 Monadnock 117 01 19-36 +0-0I 19 -'37 3-21 5-085 731 4 121 823-6 Gunstock 19 17 08 -71 -fo-56 09-27 3 -22 4 -654 798 I 45 164 -59 Wachusett 43 41 41 -10 — o-io 41 -00 3-21 4-975 287 5 94 468 60 THE MAIN TRIANGULATION. 133 Ri'sit/liiii^ cuii^/ts am! base; sides of the lrian 955 f) 81 461 99 35 14 58 -03 -0 -37 57-66 3-74 4-736 332 8 54 492 01 «5 07 29 -98 -0 -03 29-95 3-74 4-973 49' 2 94 078 -6S 99 18 37 -oS — G -26 36 -82 3 -22 4 -982 231 4 95 991. 20 34 04 13 '9' + 0-03 13-94 3-21 4-736 332 6 54 49' -99 46 37 19-03 -0-I4 18 -89 3-22 4 -849 420 I 70 70r) -11 9' 37 34-69 +0 -06 34-75 3-60 4-973 491 2 94 078 -68 48 41 42 -32 +0-50 42 -82 3-59 4 -849 420 2 70 700-13 39 40 53 'iS +0-03 53 -2 1 3-59 4-778 830 4 60 093-90 82 05 13 -39 ^-o -66 14-05 2-03 4 -849 420 1 70 700 ■ 1 1 31 GO 49 '40 +0-17 49-57 2 -02 4 -565 581 4 36 777 -43 66 54 01 73 +0-72 02 -45 2 02 4-817 279 5 65 656 -77 45 oS 44 '^5 +0 -02 44 -87 2-47 4-736 332 7 54 492 -(JO 90 36 02 -56 4-G-20 02 -76 2-48 4 -885 726 8 76 S64 -67 44 15 19 76 + -03 19-79 2-47 4-729 5t3 > 53 643 -(X) 29 59 42-88 —0-18 42 -70 1 -62 4-565 581 4 36 777 -43 46 49 04 -89 — -69 04 -20 I -62 4-729 5 '3 53 642 -99 103 II 1 8 -63 -0-66 17 -97 1-63 4 -855 073 I 71 626 -39 106 07 29-31 -fo-iS 29-49 '■63 4 -855 073 1 71 626 -39 37 18 I3'i7 +0-41 J3 -58 1-63 4-655 000 4 45 185 -64 36 34 21 -79 fo-o3 21 -82 1-63 4-647 629 9 44 425 -26 41 5S 51 '45 —0 -oi 51 -44 I -37 4 -565 581 4 36 777 -43 84 07 1 8 -06 —0 -28 17 -78 I -38 4 -737 944 54 694 -54 53 53 55-45 -0-55 54 -90 I -37 4-647 630 44 425 -27 64 oS 37-86 +0-19 38 -05 I -88 4-729 513 I 53 643 -00 49 17 23-18 -0 -I I 23-07 t -88 4 -655 000 3 45 185-63 66 34 04 -67 0-15 04-52 I -88 4 -737 944 I 54 694 -55 69 09 39-74 —0 -qS 39 -66 -70 4 -565 581 4 36 777 -43 74 40 16-66 -0 -55 16 -u -69 4 -579 231 4 37 95' -7' 36 10 06 -84 -0 -52 06 -32 -70 4 -365 932 I 23 22^ -74 130 20 20 -91 -0-49 20 -42 0-54 4 -737 944 I 54 694 -55 17 43 48-61 —0 -03 48 -58 0-53 4 -339 491 3 21 852 -01 31 55 53-18 —0-58 5- -60 ^-53 4-579 231 4 37 95' 7' 134 THE EASTERN OBLIQUE ARC. Kcsultin^ angles and sides of the triaiigtilalion between tlie lipping base net and t/ie base; also betiueen this base and the Fire Island base net — completed. 42 43 44 45 46 47 48 49 50 51 52 53 stations. Great Meadow Copecut Beaconpole r Massachusett.s North Base Great Meadow Beaconpole MassachiLsetts South Base Beaconpole Massachusetts North Ba.se Mount Tom Monadnock W chusett Bald Hill Monadnock Wachusett Mount Tom Monadnock Bald Hill Bald Hill Mount Tom Wachusett Box Hill Mount Tom Bald Hill Ivy Bald Hill Box Hill Sandford Mount Tom Box Hill Sandford Observ'ed angles Correc- tions. Splier- ical angles. Spher- ical f vSan ] i^"y 160 lO 9 70 58 51 Si 54 44 33 56 29 02 27 09 49 01 GO 06 52 28 44 59 '35 58 -27 01 "40 29 '82 15 -oi 17-42 16 -67 45 '24 58 -64 40-67 47 "59 89 46 37 '97 19 48 48-84 25-33 Box Hill Woo.ster Ivy Sandford 28 J32 95 28 55 75 62 42 65 33 80 14 34 130 31 34 114 74 56 49 53 47 78 05 05 52 39 27 16 24 19 43 25 50 48 47 24 27 16 15 02 21 35 47 40 31 49-82 53 '91 22 26 54 78 43 '62 J 3 '24 11-85 58 -37 21 -08 44-95 02 -79 46-77 14-24 27-49 43-55 55-72 34 -46 53 -03 39 -85 59-13 51 -65 14-14 +0-565 59-915 0-144 +0-566 58-836 0-143 +0-279 01-679 0-143 -0-43 -0-52 -0-33 +0-39 — o -20 +0-18 +0-04 + 1 -40 +0-71 +0-47 +0 -16 — o -II — o -43 —0-56 +0-15 — o -29 -I -23 —0-56 — o -14 — o -26 — o -09 +0-07 — o -20 — o -09 — o "19 +0-17 -0-23 O -QO — o-i8 — o -29 +0-45 +0 -25 29-39 14-49 17-09 17 -06 45-04 40-85 47-63 39 -37 49-55 25 -80 49 -98 53-80 21 -83 54-22 43-77 12-95 10 -62 57-81 20-94 44-69 02 -70 46 -84 14-04 27 -40 43-36 55 -89 34 -23 53 -03 39 67 59-42 52 -10 •4 -39 0-33 0-32 o -32 O -22 O -22 -O -08 58 -56 O -22 2 -62 2 -61 2 -62 1-78 1-78 1 -77 3-29 3-28 3-28- 2-44 2-45 2-45 I -15 I -15 1 -14 I -19 I -19 1 -20 2 22 2 -22 2 -21 2 -31 2-31 2-31 I -97 I -97 I -97 i^og. dis- tances. 4 -647 630 4-365 932 4 -339 491 4-365 932 4-324 757 4-283 145 4 -324 757 4-238 707 4-178 727 4-654 798 4 -835 503 4-913 165 4 -654 798 4-797 545 4 -995 067 4 -995 067 4-678 I So 4-913 165 4-835 503 4 -797 545 4 -67S 180 4 -678 I So 4 -459 356 4-712 792 4 -459 356 4 -808 420 4-933 714 4-712 792 4-745 910 4 -955 070 4 -808 420 4-745 910 4-707 138 4-707 13S 4 -669 1 7 1 4-791 513 Massaehusetts Distances in meters. 44 425 -27 1 23 223-74 3 21 852 -QI I 23 223 -74 7 21 123 -10 5 19 193-12 7 21 123 -lo 7 17 326-376 3 15 091 -32 I 45 164-59 I 68 470 -44 6 81 877-70 1 45 164-59 62 740 -07 2 98 870 -61 2 98 870 -61 7 47 662-93 6 8i 877 -70 1 68 470 -44 o 62 740 -07 7 47 662 -93 7 47 662 -93 2 28 797 -58 2 51 616-93 2 28 797-58 3 64 331 -00 3 85 844 -86 2 51 616-93 55 707 -03 1 90 171 -67 3 64 331 -oo 55 707 -03 1 50 949 -29 I 50 949 -29 o 46 684 -31 4 61 87474 30 CM. THFODOLITE. I 75CM. THEODOLITE. THK MAIN TRIAXGULATION. 135 ( 3. TKIANGULATION CONNKCriNC, TIIK KIKK ISLAND BASK NET WITH THK KKNT ISLAND HASK NET KXTKNDKD, CONNECTICUT, NKW VOKK, NKW JERSEY, PENNSYL- VANIA, DKLAWARE, AND MARYLAND. 1833-1845 AND 1865. The angular ineasun;s of tliis section of the (jljHque arc date from the year 1833, and were completed in 1845. The triangulation up to 1843 inclusive is essentially the work of Superintendent F. R. Hassler. In its composition it reflects the custom in those early days of including but a few composite figures, such as quadrilaterals or central figures, the chain being made up mainly of triangles. The number of observations taken would now be consid- ered as .scanty, yet with the superior instruments Mr. Hassler had procured, his results reached a fair degree of accuracy. The number of series, each including a direct and a reversed set, varied from 11 to 35, with an average of 24. At the six stations which remained to be occupied after his death in November 1843, the o1)servations of his principal assistant show an extreme range in number of series between 10 and 73. The horizontal circle of the theodolite was used at each station in several positions, most frequently in .six or three, that is, by .shifting the zero division of the graduation either 60° or 120° for each new position. It was Mr. Ha.ssler's practice to observe only at such times as were con.sidered by him favorable or conducive to good results. In 1850-51, in the local or station adjustments, the measures were treated as directions according to Bcssel's method, and an adju.stment of the triangulation was made in .sections. The results were published in the Coa.st Survey Report for 185 1, page 222, and following. Later on, in 1866-67, after the reoccupa- tion of certain stations of the Fire Island base net, and after some revision of the triangulation about the Kent Island base, a new and more systematic adjustment was made, and relative weights to the directions were intro- duced. These later results were published in the Coast Survey Report for 1866, pages 52-53. A discrepancy of 50 units in the seventh place of decimals of the logarithm of the length was developed by the triangulation, and was distributed in this adju.stment by a length equation. A compari.son of these results with the present values of the length of the .starting line Bald Hill to West Hills, .showed a difference in the logaritlnn of 4 units in the sevciUh place, whereas the new adju.stment in the vicinity of Kent Lsland ba.se showed no di.screpanc\- on the line Osbornes Ruin to Turkey Point. This fully justifieil the reteiUion of the adjustment of 1866-67, witli but a .slight change due to the No. 22. ^ashhua 'RxiLauvd, FireJsl/jTut ' WestJIiUa BiLrderi Mectingi^use Hill Buch Princivio Turkey foint Osborrwsjitiiri Firaiiy^ \ Swan Point I \ Tnylor •xc -^ Kilometers 10 O 10 20 30 40 SO St atute Miles 10 20 30 M 136 THE EASTERN OBLIQUE ARC. oradual dispersion of this small logarithmic discrepancy' of 4 units in the seventh place of decimals. The small changes indicated in the angles of the first and second triangles, which do not exceed o"'2 1 , and in the last or thirtieth triangle of less than half a second, are due to this method of producing an accord. The correction to the horizontal angles for height of stations observed upon is less than o"'o2, and generalh' this need not be considered. The approximate heights of the stations are as follows: Round Hill Harrow '■'' Buttermilk Weasel - Beacon Hill f .Springfield '^ Mount Rose Disborof .Stony Hill t Newtown I\Iount Holly The fact that the spherical excess of the triangles was computed \vith reference to the Be.sselian spheroid is immaterial, as the values from the Clarke spheroid would be the same within the limits of the size of the triangles. The details of this adjustment have not l)een publi.shed, and it is de.sirable to present here certain leading quantities, l)Ut it is essential to bear in mind that the 1866-67 adjustment started from the .sides of the triangle Tashua, Ruland, West Hills, as given, and terminated with the .side Finlay to Pooles Island. It is therefore .slightly longer than the section which is now under consideration. The small corrections to the lines Bald Hill to West Hills and Csbornes Ruin to Turkey Point, dvie to the readju.stment, are not introduced here, but the effect is indicated bj' the fractional seconds placed in parenthesis and already alluded to above. The mean error of a triangle, derived from the sum of the .squares of the clo.sing errors, V73'g2 = zt i"'50, and that of an angle =h o"'86, and the probable error of a The probable error of a direction, f^, as found elers. Feet Meters. Feet. 177 582 Willowgrove 132 433 116 379 Pine Hillf 6r-4 202 217 712 Yard 150 493 178 5S3 Lippincott 43 142 II37 373 Bethel 125 410 159 523 Burden, less than 500 1277 419 Meetinghouse Hill less than 500 84-2 276 Buck, less than 500 71-6 235 Principio, less than 500 99 326 Turkey Point 25 82 55-3 181 Osbornes Rviin 90 295 33 direction eqitals 0^674 — ^ n/6 ■41. approximately from the individual measures at each .station, is d=o"'25; hence the .square of the triangle-combination error = tj = (o'4i )' — (o'25 )''= 0*107, which quantity was I „,,„_. Aipi^^ ratio of the greatest to the least value of— is added to each f ^ as o'63 to o'i2. hence P +v p ^^ Delerniiiied in 1.S17. t Result of spirit leveliuj; THE MAIN TRIANGULATIOX. 137 Abstracts of horizontal directions at the principal stations l>etween the Fire island and the Kent Island- base nets, Connecticut, Nezv York, New Jersey, Petinsylvania, Delatvare, and Maryland, /8jj-/Sfs and /S6j. Hald mil, I'airfield Count}', Coiinecticul. July 23 to Auj^ust 18, 1.S33. 60'" direction theodolite Nf). 2. I', R. Ilassler, observer. Num'Der of (iirec- Objects observetl. tions. KcsuUiiifi direction from station adjust- ment. Approxi- mate prot)- able error. Keduc- lions to sea level. Correc- Correc- -— - •sii:^ \^, s<^;ris. adjust- ment. justmeiit of 1S66. Tashua' Kuland* 8 West Hills 9 Harrow Round Hill O 00 62 40 99 31 121 42 i.SS 36 Circle iTSed in VI positions. 00 '000 17 '802 +" -056 40 '''35 lS'6o9 54 -002 o '60 -t-o'cx)6 — O'lOJ + 1 '433 0'27 .... o'ly .... "40 .... Mean correction 0"372 (59 '903) (14 -291 J -o'2I3 (40-622) +o'434 -0'954 41-27 17-65 53 9 1 [Vest Hills, Suffolk Count)', New York. Octolier iS to December r. rS36.t 75 "" direction theodolite No. I. F. R. Hassler, obser\-er. Jul}' 18 to Autju.st 15, 1S65. G. W. Dean, olj.server. direction theodolite No. i. Wooster 00 . 00 -000 ±0-06 - -ooj 4-0 -169 (00-166) 'X)I7 Azimuth Mark 7 26 21 -76S 0-06 (21-781) Tashua t 21 35 06 -476 0-05 -1-0 -006 -0-099 (06-3S3) Sandford 33 ss 36 '531 o-oS -(-0-0I4 -0 -089 (36-456) Rulandt Sg 14 44741 0-32 +0-226 (44 967) Fire Island E;ast Ba.se % 122 36 15 '675 0-33 — o'40o (15-275) Fire Island West Basel '43 5S 00 'SoS 0-38 +0-406 (01-214) 3 Harrow % 269 17 04 •25'' o-i6 +0 ■055 04-3! 4 Round Hill t 331 59 49-211 o'33 +0 ■314 49 -52 5 Bald Hint 359 21 01 -916 0-25 Meai —0 -003 correction -0. 123 0-013 (01.790) — log 01 -Si MoiDul Hill, Fairfield Count}-, Connecticut. July 5 to i.S, 1S33. F. R. Hassler, observer.;! 60"" direction theodolite No Number of directions. Objects obser\'ed. Results from sta- tion adjustment . .-approxi- mate proba- ble errors. Corrections from adju.st- nient of iS66. Final seconds II 12 13 14 Bald Hill West Hills Harrow Buttermilk || o 93 121 220 00 -QOO ,^1^ 594 34 -930 52 -250 -3 '560 ±0-25 0-30 O '26 o '38 • 0-275 — I -264 +0 -965 -o-iSi 00 '27 37 '33 35 -J-ig 4^-51 *The correction refers to Rulaiid station of 1S65. t Twenty-six series were ol»ser\'ed in 1S56. I Hassler, observer. ? Fourteen series were ohser\-ed. II The reduction indicated is on observer's authoritv. 138 THE EASTERN OBLIQUE ARC. .-l/)s/nuis of Iiorizontal dhcdiouF. at the piincipal stations between the Fire Island and tlie Kent Island base nets, Coiiuecticnt, Nea' York, Neza Jersey, Pennsylvania, Delaware, and Maryland, /Sjj-/S^j and /S6j — continued. Harnnc, Queen's County, New York. November lo to December 12, 1S37. 75 '^'" direction theodo lite No. I. F. R. Hassler, ob.server. Twenty-four series were taken. Xumlier of directions. Objec 18 Beacon Hill 19 Springfield 20 Weasel * 2: Buttermilk 22 Round Hill 23 Bald Hill 24 West Hills Results from sta- Approxi- Corrections mate proba- from adjust- ble errors. ment of 1S66 / // // // 00 00 "GOO ±0-31 + '060 32 08 GO 764 0-37 +0 -438 54 02 55 -302 -I -032 0-24 —0 -058 no 3S 12742 0-I7 -0-133 128 21 16-936 •16 —0 '071 U9 34 06715 0.34 —0 -230 217 19 34 '439 0-41 -f 0-213 Final seconds. 00 '06 01 '20 54-21 12 'Gl 16-86 06 -48 34-65 Buttermilk, Westche.ster County, New York. June 11 to 29, 1833. ec™ direction theodolite No. 2. F. R. Hassler, ob.server. Eleven .series were taken. 5 Round Hill 6 Harrow 7 Weasel 00 fX) -000 zhO -22 -to -098 OO'IO 63 46 44 -026 -22 4-0 -184 44-21 37 17 19-193 0-23 —0 -291 18 -90 Weasel, Passaic County, New Jersey. September 19 to October 23, 1838. 75"" direction theodolite No. I. F. R. Hassler, ob.server. Nineteen series were taken. 25 Buttermilk 26 Harrow 27 Beacon Hill 00 00 -000 ±0 -22 +0 -235 oa-23 49 54 10-775 -24 +0 -loo JO -87 133 03 ! I -643 "20 -0-312 11-33 Spr2ni;Jield, Union County, New Jersey. November 6 to 24, 183S. 75"" direction theodolite No. i. F^. R. Hassler, observer. Twenty series were taken. 33 Harrow 34 Beacon Hill 35 Mount Ro.se 00 00 -ooo ±0 -22 -0 -348 59-65 84 13 25 -129 o-j8 + 0-324 25-45 142 41 14 -780 -21 -0-013 14-77 Beacon Hill, Monmouth County, New Jersey. July 8 to 24, 1839. Theodolite No. i. F. R. Hassler, observer. Nineteen .series were taken. 28 Disboro 29 Mount Rose 30 Springfield 31 Weasel f 32 Harrow 00 00 -ooo ±0 -21 -fo-oi6 00 02 35 06 41 -283 -24 —0 -091 41 -19 108 40 25-771 -21 — 0-267 25 -50 129 30 52 -007 -20 +0 -266 52-27 172 19 04 -232 0-17 T-O -056 04-29 *-rhe correction is for eccentricity. t Angle between Weasel and Azimuth Mark, 3° 35' 36"'95±o"-40 . THE MAIN TRIANGULATIOX. 139 Abstracts 0/ horizontal directions at the principal stations between the Fire Island and the Kent Island base nets, Connecticut, New York, Nerv Jersey, Pennsylvania, Delaware, and Maryland, /Sjj-/8^f5 and /cSY)5 — coiilimieil. Disboro, Mercer County, New Jersey. August 11 to 28, 1839. 75"" 'lireclioii theodolite No. i. K. R. Hassler, observer. Eijlmciil. Approxi- mate proba- ble errors. Corrections from adjust- ment of 1S66. c / // // // OC) CXJ '(XDO ±0-33 -0 472 73 07 29 710 f) -29 — 296 117 05 58-189 016 -0 093 152 06 60 -223 -22 - -629 237 35 4« -'"iSS (,■26 -0 ■49o3) 0-409 — -461 (31) 147 +0 -266 (68) 0-133 —0 -461 (104) 0-283 + 0-414 (32) 0-136 +0 -056 (69) - 1 24 -0 -257 ('05) (33) 0-155 -0 -348 (70) 0-129 +0-521 (106) -124 + 0-I24 (34) 0-139 +0 -324 (71) 0-175 +0 -262 (107) 0-147 + 0-077 (35) 0-151 - -013 (72) 0-139 -0-223 (loS) 0-625 — I -ICO (36) 0-155 -0 -097 (73) 0-160 +0 -442 (109) (37) 0-133 + - II 9 Vi6-7 " = ±0 "47 Resulting angles and \ No. Stal Round Hill Bald Hill West Hill.s Harrow Bald Hill West Hills I Harrow Round Hill West Hills I Harrow Round Hill Bald Hill IButterniilk Round Hill Harrow I Weasel Buttermilk Harrow I Beacon Hill Weasel Harrow {Springfield Harrow Beacon Hill f ]Mount Rose 9 I Springfield [ Beacon Hill IDisboro Springfield Beacon Hill IDisboro jNIount Rose Beacon Hill 4192 — No. 7 — 02 THE : M AIN T] RIANGU LATIC )N. 145 s of 11 u- hi an ijHlation between the Fin Island base net and the extended )ict ^f the Kent Island base. Observed aiiKles. Correc- tion. Spher- ical angles. Spher- ical excess. I.oj;. dis- tances. iJistances in meters. / // // // // 93 33 38 '59 -I -54 37-05 0-66 4-648 135 6 44 477 -oi 59 <'5 '3 ''7 (■38) -0-52 .2-65 0-66 4 -582 434 I 38 232 62 27 21 12 70 ( -58) —0-42 12-28 0-66 4-311 236 3 20 475 -58 67 45 2772 +0-45 28 -17 0-68 4 -648 135 6 44 477 -01 22 10 37 77 ( -58) -I -39 36 -38 0-68 4 -258 590 2 18 138 -03 90 03 57 "65 (•54) —0 -16 57 -49 0-68 4-681 716 2 48 052 -52 SS 5S 17-50 +0-28 17-78 0-52 4-582 434 1 38 232 -63 28 18 56-34 + 2-23 58 -57 0-52 4 -258 590 2 18 138 -03 62 42 44-95 -ro -26 45 21 -52 4-53' 267 4 33 983 -45 21 12 49 -78 —0 -16 49-62 -50 4-311 236 3 20 475 -58 121 52 34-93 +0-69 35-62 0-50 4-681 716 2 48 052 -52 36 54 35-39 +0-87 36-26 0-50 4-531 267 4 33 983 -45 63 46 44-03 -fo-09 44-12 0-33 4-531 267 4 33 983 -45 98 30 13-76 -I -15 12 -61 0-33 4 573 62S 3 37 465 -22 17 43 04-19 +0 -06 04-25 0-32 4 -061 771 2 II 5 28 -46 49 54 10 78 -0-14 10-64 1-24 4-573 62S 3 37 465 -22 73 30 35-17 —0-48 34-69 I -24 4-671 752 6 46 962 -65 .56 35 18-47 —0-07 iS -40 I -25 4-611 542 6 40 S82 -98 42 48 12 -22 — -21 12 -01 2 -20 4-671 752 6 46 962 65 S3 09 GO '87 -0-41 00 -46 2 -21 4 -836 466 7 68 622 -52 54 02 54-27 —0 -12 54-15 2 -21 4-747 798 S 55 949 -84 84 '3 25-13 + -67 25 -80 1 -91 4 -836 466 7 68 622 -52 32 08 00 76 + 0-38 01 -14 I -91 4-564 498 I 36 685 -Si 63 38 38 -46 +0-32 38 -78 I -90 4-791 (X19 9 61 803-04 47 58 30-19 —0 -06 30-13 1 -25 4-564 498 I 36 685 -Si 5S 27 49-65 -0-34 49-31 1 -25 4-624 192 9 42 09' -36 73 33 44-49 — o-i8 44-31 1 -25 4-675 473 3 47 366 -72 44 09 20-94 -f -20 21 -14 071 4 -564 498 I 36 6S5 -81 27 TO 15 -49 -70 4-381 0S6 I 24 04S 39 loS 40 25 -77 —0 -28 25 -49 0-71 4-698 022 4 49 891 02 U3 12 55 -47 —0 -03 55 -44 0-50 4-624 192 8 42 091 -35 31 40 24 90 — -03 24 -87 0-49 4 -381 »>86 I 24 04S -39 35 ID 06 41 -28 — o-ii 41-17 0-49 4 -420 656 6 26 342 48 146 THE EASTERN OBLIQUE ARC. Result ins: ans'lcs and side of the triangulation betzveen the Fire Island net of the Kent Island base — continued. base net and the extended 14 15 16 17 18 19 23 stations. Ob.se rvec angles. Correc- tion. ical angles. .^pner- ical excess. Log. Dis- tances. Distances in meters. / // // // /' Disboro 69 03 34 '53 -0.-23 34 -30 I -04 4-675 473 2 47 366-71 Mount Rose 79 38 55" 10 — OTO 55-00 I -04 4-698 022 4 49 891 -02 Springfielil 3t 17 33 -82 r -04 4-420 656 6 26 342 -48 vStony Hill 60 40 1 1 -86 1 0-14 12 -QO 0-39 4-420 656 6 26 342 -48 Mount Ro.se 35 36 10 'oS -\ -17 10-25 o'39 4-245 277 5 17 590-47 DLsboro 83 43 3870 -i-O -22 38 -92 0-39 4-477 626 30 034 -89 Mount Holly 45 45 41-98 4-0 -88 42 -86 0-54 4-477 626 30 034 -89 Mount Rose 3' 38 20 -41 -0 -05 20-36 0-55 4 -342 240 8 21 990-79 Stony Hill 102 35 57-94 +0 -48 58 -42 0-55 4 -611 856 8 40 912 -58 Newtown 4! 12 36 -26 + I-I5 37 '41 0-54 4-342 240 8 21 990-79 Stony Hill 63 09 51 -29 +0-87 52 -16 0-53 4-473 984 7 29 784-12 Mount Holly 75 37 30-71 + 1 '33 32-04 o-,54 4 -509 657 7 32 333 -87 Newtown 105 37 14-25 4- -67 14 -92 0-51 4 -611 856 8 40 912 -58 Mount Rose 44 30 57-51 —0-07 57-44 0-51 4-473 984 7 29 784-12 Mount Holly 29 51 48-72 4-0 -45 49 '17 0-51 4 -325 374 2 21 153-11 Newtown 64 24 37-99 —0 -48 37-51 0-52 4-477 625 9 30 034 -88 Mount Ro.se 76 09 17-92 — '12 17 -80 0-52 4-509 657 7 32 333 "87 Stony Hill 39 26 06 -64 -0-39 06-25 0-52 4 -325 374 2 21 153-11 Willowgrove 67 07 37-54 -0-49 37-05 0-48 4 -473 984 7 29 784-12 Newtown 74 53 42-14 — I -10 41 -04 0-48 4-494 280 7 3 1 209 -06 Mount Holly 37 58 44-27 — -91 43 -36 0-49 4 -298 685 8 19 S92 -33 Pine Hill 51 44 1S-18 4-0 -48 18-66 0-75 4-494 280 7 3 1 209 -06 Willowgrove 46 05 54-33 +0-16 54-49 0-75 4-456 957 7 28 638 -99 Mount Holly 82 09 48 -44 +0-66 49-10 0-75 4 -595 230 7 39 375 -92 Yard 33 40 18 -81 +0 -20 19-01 0-93 4 -456 957 7 28 638 -99 Mount Holly 48 51 18 -62 1 -85 =9-47 0-94 4 -589 931 4 38 898 -37 Pine Hill 97 28 24-19 + -12 24-31 0-93 4 -709 403 7 51 215-76 Lippincott 85 28 48 -61 + I-I2 49-73 -69 4 -589 931 4 38 89S -37 Yard 47 24 56 -37 + -78 57-15 -70 4 -458 328 4 28 729-52 Pine Hill 47 06 14-53 + -67 15 -20 -69 4-456 145 5 28 585 -48 Bethel 35 15 32-01 — -46 31 '.55 0-43 4 -458 328 4 28 729 '52 Pine Hill 24 14 38 -80 -Q-IO 38-70 0-43 4-310 393 7 20 435 -90 Lippincott 120 29 50-65 + 0-39 51 -04 0-43 4 -632 282 7 42 S82 -76 Bethel 100 16 49 "45 -|-0 "20 49 '65 0-28 4 -456 145 5 28 585 -48 Yard 44 42 10-15 —0-26 09-89 -29 4-310 393 7 20 435 -90 Li])pincott 35 01 02-03 -0-72 01 -31 0-28 4-221 948 9 16 670 -51 THE MAIN TB JANGULATIO N. 147 Res tdtin_s; angles ami sides of Ihe li-iaiig Illation lyetiueen 11 e /'ire /stand Itase net ana ' the ex ■tended net of Ihe k'eiit Island l>ase — continued. No. stations. ()l>serve( aiiKles. Correc- tion. Spher- ical angles. Spher- ical excess. Ix>g. dis- tances. Distances in meters. / // // // // ' Bethel 65 01 17-44 -|c) -67 18-11 -55 4-589 93' 4 38 898 -37 24 . Yard 92 07 06-51 { -52 07 -03 "•55 4 -632 282 6 42 882 -75 Pine Hill 22 51 35 '74 -fo-77 36 -5 1 0-55 4-221 94M 9 ;6 670-51 Burden 30 04 36 -80 —0 -30 36 -5') 0-34 4-310 393 6 20 435 -89 25 Bethel 32 49 26-82 —0 -I r 26 -71 -34 4 -344 465 5 22 103 -73 Lippincott 117 05 58-19 - 0-3S 57 ■■^' 0-34 4-559 9'4 6 36 3or) -67 ' Meetinghouse Hill 37 23 53 -26 —0 •70 52 -56 -61 4 -344 465 5 22 '03 -73 26 Lippincott 73 07 29-71 -0-77 28 -94 -61 4-541 914 f) 34 826 -V, ^ Burden 69 28 40-92 -0-59 40 -33 -61 4-532 554 6 34 084 -32 ' Buck 86 45 35-31 +0-31 35-62 -49 4-541 913 9 34 .S26 -82 27 . Meetinghouse Hill 59 5' 56 -89 +0-63 57-52 0-49 4 -479 550 7 30 168 -29 Burden 33 22 27-S5 +0 -48 28 -33 0-49 4 -283 056 5 19 189 iS Principio 41 47 41 -53 +0 -38 41 -91 •3« 4 -283 056 5 '9 1S9-18 28 Meetinghouse Hill 56 59 06 -22 -fo-oi 06-23 0-39 4-382 796 24 143 -27 Ruck Si 13 12 -91 +0 -11 13-02 0-39 4-454 159 6 2,S 455-06 Turkey Point 65 21 20-56 —0-03 20-53 -32 4-382 796 24 143 -27 29 Principio 77 37 28 -45 -0-14 28-31 0-32 4-414 063 I 25 945 56 Buck 37 01 12-45 -0 -34 12 12 0-32 4-203 937 I 15 993 26 30 Osbornes Ruin Principio 35 57 10 36 II -67 (II -78) 57-66 —0 -40 —0 -26 II -27 57-40 0-31 -32 4 -203 937 4-370 101 r 8 15 25 995 26 447 -78 Turkey Point a? 12 52-52 (52 -96) -0-24 52 -28 0-32 4 -443 000 9 27 733 -26 148 THE EASTERN OBLIQUE ARC. No. 23. iJfump b CLC Tc Spt 'Tobi I Row .ong kFlat Top Smith Mt. (BuJFaZo Moore^ Kilometers o 10 20 30 Statute Miles j-l i-i i-i-ca- 4. FIRST SECTION OF THE TRIANGULATION, SOUTH OF THE TRANSCONTINENTAL TRIANGULATION, IN VIRGINIA AND NORTH CAROLINA, 1875- 1879. In connection with the account of the Kent Island base net and its extension to the westward there are given the abstracts of the horizontal direc- tions as well as the adjusted angles and triangle sides between the triangulation stations which connect that base with the sides of the triangle Humpback, Tobacco Row, Spear. It is from this triangle that the triangulation of the oblique arc departs from that of the arc of the parallel and the first section, proceeding to the southward and west- ward, terminates at the line Buffalo to Moore. Between Humpback and Moore the triangulation is so strengthened by the numerous tie lines that it is not supposed that any measurable error could accumulate within this section; its whole adjust- ment was therefore made to depend for initial direction and length on the above fixed triangle. In this section there are 24 conditions to be sat- isfied and 42 directions to be corrected. The approximate elevations of the stations are as follows: Humpback Spear Tobacco Row Long Mountain Flat Top Cahas Smith ]Mountain Moore Buffalo Meters. I 1 10 "4 491 7 S94 ■ S 436-8 I 21S7 I 088 '4 622 7 784 -o I 210-4 Feet. 3 643 1 613 2 936 1 433 3 998 3 571 2 043 2 572 3 971 Corrections to horizontal directions for height of station observed upon were applied. Squaring the closing errors of the triangles we get-w — 28 i"-52 as the mean error of a triangle, also mean error of I '^2 an angle —f- — dszo"-9,S and the probable error of a direction =ito"'42. THE MAIN TRIANGULATIOX. 149 /Ihsirads of horizontal dnrcHo)n al stations tonipositijr the first section of the trianfridation south of the t ran scon tiuen tat triangutation, /Sy; to iSjg. I/uinpbac/c, Nelson County, Virginia. June 8 to 29, 1875. A. T. Mosnian, observer. 35"" direction theodolite No. 10. May j i to June 6, 1S78. A. T. Mosman, observer. 50'-"* direction theodolite No. 114. August 18 to 28, 1879. A. T. Mosnian and W. B. Fairfield, obsers-ers. 50"" direction theodolite No. 114. No. of direc- tions. Objects observed. Corrections Corrections from ad- kesMltsof local ^T/" f.!:'"';'; KesultinK Reductions KesultinK :,;™"' li'/^f adjustment. 'Jninsc'mti *^'^™nds. tosea level, seconds. ^"^"fiV^"'"^ nental arc. Final seconds. Jarman Spear I/g (orrei 'ales. c.= + •190 c,= = + ■767 c..= = — •196 c.= +0 •547 C,o = = — •844 C.8 = =+0 •0145 C3 = + •093 c„= = +0 •134 c.,= = — •0569 C4 = -0 ■183 c„= = +0 •146 C.o= =— •603 C5 = — •5S7 C,3 = = +0 ■276 c=.= =+0 •0231 C6 = — ■554 C.4 = :— •842 c..= = — •285 C; = + •231 Cx5 = = +0 •051 c„= =+0 •0233 C8 = 4-0 •28S C,6 = = + -129 C.4 = = + •0665 Resulting eo) rectious to obs crved direetioii S". (0 = = +0 -460 (12) = = — 0"24I (23) = = -^ •130 134) = = —0-146 (2) +0-251 (13) +0 -836 (24) — •187 (35) -0-445 (3) -0 -079 (14) -0 -495 (25) -t-o •176 (36) —0 039 (4) -0 -326 (15^ — 0-281 (26) -^0 •062 (37) -0 -384 (5) -0 -075 (16) -0-134 (27) — ■176 (38) -fO'lOO (6) +0 -068 (17) —0 -112 (28) — •479 (39) —0 -230 (7) -0 -869 (18) -0 -077 (29) +0 •359 (40^ - 1 -483 (S) + 0-926 (19) ^0 -089 (30) — ■377 (41) -0 -576 (9) + -468 (20) +0 -398 (31) + 1 •06S (42) -0 -677 (10) -0 -471 (21) +0 -118 (32) — 061 (") -0-097 (22) +0 -474 (33) — •842 Probable error of an observed direction o 674 ^/ ^- — =3tO -41. 154 THE EASTERN OBLIQUE ARC. I\CS!ill!)ig aiiglis and sidts of Long Mountain Humpback Spear Tobacco Row Humpback Long Mountain Long Mountain Tobacco Row Spear Flat Top Tobacco Row Spear Flat Top Spear Long Mountain Flat Top Tobacco Row Long Mountain Smith Mountain Tobacco Row Spear Smith Mountain Spear Long Mountain Smith Mountain Flat Top Tobacco Row vSmith Mountain Tobacco Row Long Mountain Smith Mountain Flat Top Spear Smith Mountain Flat Top Long Mountain the first section of the triaugulatioii net and extension. sont/icuest of the Kent Island ttase Observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. Log. dis- tances. Distances in meters. o / // // 1/ // 30 47 57-98 -I -33 56-65 I -35 4-649 2S3 4 44 594 -71 2.S 27 31 "65 +0-46 32-11 I '35 4-618 077 4 41 502 -80 120 44 35 '53 -0-25 35-28 1-34 4-874 224 9 74 855 -71 132 04 13 '13 -0 -qS 13-05 1 -00 4 -874 224 9 74 ■855-71 iS 24 0970 —0 -46 09 -24 0-99 4-502 886 6 31 833 -66 29 31 39 '61 + 1 -08 40-69 0-99 4-696 339 6 49 698 -08 60 19 37-59 -0 -25 37-34 0-97 4 -577 326 2 37 785 -59 72 37 0879 —0 -07 08 -72 0-98 4-618 077 4 41 502 -So 47 03 17-11 -0-25 16 -86 0-97 4-502 886 7 31 833 -67 10 J7 00-23 +0-15 00-38 -41 4-577 326 2 37 785 -59 159 40 31 -48 fo-92 32-40 -41 4-866 398 9 73 518-88 10 02 28 -12 +0-33 28 -45 -41 4 -567 083 6 36 904 -86 31 44 51 -50 +0 -02 51 -52 1-56 4 -618 077 4 41 502 -80 37 oo 48-99 -0-57 48-42 1-56 4-676 543 I 47 483 -54 III T4 25 -12 -0-39 24-73 I -55 4 -866 398 9 73 518 -88 42 01 51 -73 +0-17 51 -90 0-99 4-502 886 7 31 833 -67 ft7 03 22 -69 + 1 -00 23-69 I -00 4-676 543 2 47 483 -55 50 54 47-53 —0 -14 47-39 0-99 4 -567 083 6 36 904 -86 20 50 35 -03 —0 -24 34-79 I 96 4-577 326 2 37 785 -59 118 II II -60 +0-07 II -67 I -97 4-971 303 I 93 605-87 40 5« ^9-35 +0 -08 19-43 I -96 4-842 815 4 69 633 -05 4 48 " -73 —0-30 11-43 0-35 4-61S 077 4 41 502 -80 6 04 57-76 -0-33 57 -43 0-35 4 -720 334 2 52 521 -14 69 06 53-16 -0-97 52-19 0-35 4-971 303 93 605 -85 30 12 41 -15 —0 -11 41 -04 I -44 4-567 083 6 36 904 -86 108 18 02 -34 +0 -20 02-54 I -44 4-842 815 2 69 633 -02 41 29 19-88 +0 -86 20-74 I -44 4-686 522 8 48 587 -30 25 3« 46-76 -0-55 46 -21 1-34 4-502 886 7 31 833 -67 45 34 02-81 +0-14 02-95 1-34 4-720 334 4 52 521 -17 loS 47 15-57 --0-71 14 -86 ' -34 4 -842 815 4 69 633 -05 51 03 16-18 -0-35 >5 -83 3-00 4 -S66 398 9 73 51S-88 98 01 02-11 +o-o6 02 -17 2-99 4-971 303 I 93 605 -87 30 55 5f -23 —0 -24 50-99 3-00 4 -686 522 9 48 587 -31 55 5> 27 -91 -0 -66 27-25 1-79 4-676 543 2 47 4S3 -55 66 16 10 -61 +0-03 10 -64 I -79 4-720 334 3 52 521 16 57 52 2S -04 -0-56 27-48 I -79 4-686 523 48 587 -33 No. '3 14 15 16 17 IS 19 23 24 THE M AIN TI ilANGU LATIC >N. ^5S Itiyii^ angles and sides (if the first scclion of the Iriangu lation southwc v/ if the Kent Island fiase Ul ■/ a)i d extension — continued. Stations. (Jhservcc aiiKles. Correc- ti4 I 0-23 39 "37 2-28 4 -946 643 2 88 438 -88 Cahas 30 45 1012 fo-71 10 -83 I 96 4-676 543 2 47 483 -55 Flat Top 114 08 02 -56 H "-51 03 -07 I -96 4 -928 119 6 84 746-08 Long Mountain 35 06 51-61 +0-37 51 -98 1-96 4-727 663 6 53 415 05 Cahas 59 5S 52-64 --(J -42 52-22 1-63 4 -686 522 9 48 587-31 Flat Top 47 51 51 '95 i-o -48 52-43 ■ -63 4-619 220 5 41 612-18 Smith Mountain 72 09 19-88 -f -36 20 -24 ■■63 4-727 663 5 53 415-04 Cahas 29 '3 42-52 -I -'3 41 -39 1 -46 4-720 334 3 52 521 -16 Long Mountain 22 45 36-43 —0-94 35-49 i -46 4-619 220 5 41 612-18 Smith Mountain 128 00 47 '79 —0-30 47-49 1 -45 4-928 119 6 84 746-08 Cahas 50 16 22 -02 +032 22 -34 2 40 4 -842 815 4 69 633 05 Tobacco Row 27 21 44-51 -0-94 43 -57 2 -40 4-619 220 6 41 612 -19 Smith Mountain 102 22 01 -03 +0-25 01 -28 2-39 4-946 643 3 88 438 -90 Buffalo 25 52 26-05 +0 -83 26-88 3-38 4 -686 522 9 48 587 -31 Flat Top 49 35 42-73 +0-19 42-92 3 -38 4 -928 312 3 84 783-69 Smith Mountain 104 32 GO -28 +0-05 00-33 3 -37 5 -032 535 107 779-2 Buffalo I 41 55-85 H0-41 56-26 0-15 4-727 663 5 53 415-04 Flat Top I 43 50-78 -0-2S 50-50 0-15 4 '735 698 3 54 412-45 Calias 176 34 13 18 +0 -50 13 -68 0-14 5 -032 534 9 107 779-2 Buffalo 24 10 30 -20 ■ 0-42 30 62 1 -60 4-619 220 5 41 612-18 Flat Top 123 26 54-18 -08 54-10 I 60 4 928 312 3 84 7S3 -69 Smith Mountain 32 22 40-40 -0-32 40 -oS I 60 4 -735 698 6 54 412-49 Moore 15 03 54-82 —0 -10 54-72 2-73 4 -686 522 9 48 587 -31 Flat Top 30 05 II -79 -10-17 1 1 -96 2 73 4-971 803 6 93 713 -Si Smith Mountain T34 5" 01 -82 —0 -30 (11 -52 2-74 5-Ii2 329 4 I ^2 534 -6 Moore II 17 38 -02 -2 06 35 96 1 -'X^ 4 727 663 5 53 415-04 Cahas 15 J 55 50 -26 — 1 -20 49 -06 1-83 5-122 329 5 132 534 -6 Flat Top 17 46 40 - 1 6 4 "-3' 40-47 1 -83 4 -920 554 4 83 2S2 -62 Moore 26 21 32 -84 -2-i6 30 -68 2-93 4-619 220 5 41 612 iS Cahas 90 56 57 -62 — 0-7S 56 -84 2-94 4-971 803 6 93 713-81 Smith Mountain 62 41 41 -94 -0-66 41-28 2-93 4 920 554 3 83 282 60 156 THE EASTERN OBLIQUE ARC. No. 25 26 27 Itinff angles and sides of the fir. / sec lion of the triangulation southwest of th ■ Kent Island base n 't at d extension — continued. stations. Obser\-ed insjles. Correc- tion. Spher- ical anarles. Spher- ical excess. Log. dis- tances. Distances in meters. / // // " // Moore 49 iS 52 -89 -0-35 52 -54 4-04 5 -032 535 107 779-2 Buffalo in 10 48-06 -F -55 48-61 4-04 5-122 329 3 132 534 -6 Flat Top 19 30 30-94 +0-03 30 -97 4-04 4-676 356 4 47 463-13 Moore 3S 01 14 -87 + 1-71 16-58 2 -06 4-735 698 6 54 412 -49 Buffalo 109 2.S 52-21 +0-14 52 -35 2 -06 4 -920 554 3 83 2S2-60 Cahas 32 29 56 -56 f -69 57-25 2 -06 4-676 356 4 47 463-13 Moore 64 22 47 7 [ -0-45 47-26 3-40 4-928 312 3 84 783 -69 Buffalo W5 18 22 -oi -0-28 21 -73 3-39 4-971 803 6 93 713-81 Smith Mountain 30 19 or -54 -0-34 01 -20 3-40 4-676 356 4 47 463-13 No. 24. 5. SECOND OR NORTH CAROLINA SECTION OF THE TRIANGULATION SOUTH OF THE TRANSCONTINENTAL TRIANGULATION, IN VIRGINIA AND NORTH CAROLINA, 1876- 1895. This section extends over an area covered by several large tri- angles which have the centrall}' located station Poore as one of their points in common. In 1878 when the main triangulation be- tween the lines Buffalo to Moore and Grassy to Sawnee was ad- justed, this central figure about Poore had no existence. In con- sequence of the introduction of this figure some modification in the treatment of the work be- tween the Kent Island and At- lanta bases became necessary. The adjustment of 1878 involved considerable labor, as it included the formation and solution of 41 normal equations. It was de- sirable to retain this adjustment and interpo.se the central figure about Poore for the purpose of disposing of whatever error was developed between the bases by the intervening triangulation. The probable error of the meas- ure of the Kent Island base, which is the least accurate of the six bases along the arc, is 34 units in the seventh place of decimals of its logarithm, whereas that of the Atlanta base is but 10 units; Bixffbdo / V . — /A Rogers^__ / /\ ' /\ iMoore\ / \ / jf^ yRoan High Bhi/T \ /^^^ \ \ -^KFaure \ /7_ -"^yYouTig Benri. \ / / y^ing KUometers 10 iO 20 30 40 50 60 70 80 90 100 UO 120 UO IV) 150 Statxite Miles 10 10 20 M 40 50 60 70 80 90 THE MAIN TRI ANGULATION. 0/ hence the influence of the latter over tlie trianj^ulation between stations Sawnee and Benn, which constitutes the third section, was retained. In the present central fij^ure the condition was introduced preserving the fixed relation between the two sides marked in the diagram by heavy lines. The approximate elevations of the stations are as follows: Poore Young Benn eters. Keet, 817 2 680 King 333 I 093 Roger.s 886 2 907 Roan Higli Bluff Meters. Feet. 516 I 693 I 746 5 729 I 913 6 '/O From the eleven triangles we derive the mean closing error of a triangle /56-8_ ' II 2 '27 2""27, the mean error of an angle — 7= ^3 zb I "'5 1 and the probable error of a direc- tion o'674 2'27 ± o"'63. In the preceding diagram, the two heavy lines are fixed in length, and the disper- sion of the di.screpancy between the bases, of 24 units in the .seventh place of decimals in the logarithm, is accomplished by the adjustment. Attention is called to the fact that in a figure adjustment, when forcing an accord l)etween the fixed lengths of two ter- minal sides, as is the ca.se here, the conditional eqriation may be established either with plane angles or with spherical angles, provided in the latter case the terminal sides are corrected for difference between arc and sine. This is readih- done by means of the table given in Coast and Geodetic vSurvey Report for 1894, Appendix Xo. 9, page 289, below the heading "Table of corrections to longitude for difference in arc and .sine." In e.stabli.shing the length equation for any unadjusted figure the apparent dis- crepancy to be dispersed in order to produce accord between two lines who.se length is fixed will vary with the angles selected. The true discrepancy to be dispersed can, lievertheless, be obtained from the length equation, provided the length equation l^e taken last in the .solution of the normal equations, thus eliminating all the other unknown quantities; and the di.screpancy so derived is the same as would beobtained if the length equation were formed after the entire figure had been adjusted in all other respects. In the present .section the length di.screpancy with the uncorrected .spherical angles was 78 units; but the true di.screpancy out.stauding after the other adjustments are made is but 24 units. This is less than the probable error of the mea.surement of the Kent Island base. The logarithm of the length of line Buffalo to Moore is4"676 356 4, and that of the line Benn to King, 4'705 136 6. 158 THE EASTERN OBLIQUE ARC. Abstracts of hoyizontat directions at stations composing the second or North Carotina section of the triangiilation , /Syd-iSg^ . Buffalo, Floyd County, Virginia. September 25 to October 16, 1S76. 35 ^™ direction theodolite No. 10. A. T. Mosman, oVjserver. September 27 to October i, 1S95. 45^™ direction theodolite No. 4. A. H. Buchanan, observer. ^^1 Objects Observed. Corrections Corrections D 1* „r 1 „„i R.euuc- D„^, ,,,;„„ from ad- Result- from ad- „•. „, Reduc- tions to sea level. first sec- tion. onds. second sec- tion. (48-98) O GO 00 •QO .... 41 36 48-92 —0-04 62 51 49 -89 70 37 50-34 +0-01 99 35 20-42 +0-05 144 29 13 -76 +0 -04 290 26 00-73 +0 '09 292 07 56-59 -fo-o8 316 18 26-85 +0-02 Probable error of a single observation of a direction { /). and A".), (Buchanan, observer), c, = ± i"-25. Circle used in XI positions. Bull Mountain Moore Pilot Mountain 3 Young 4 Poore t 5 Rogers *t Flat Top Cahas Smith Mountain 48 -88 50-35 20-47 13-80 00 -82 56 -67 26 -87 — o -63 —0-19 +0-74 -0-44 — o -04 +0-38 (00-38) (56-63) (27 '25) 49 72 ■ 20 -28 14 '54 Moore, Stokes County, North Carolina. November 7 to December 26, 1876, and April 21 to May 31, 1877. 35^"' direction theodolite No. 10. A. T. Mosman, observer. Pilot Mountain on on -on Buffalo 89 04 10 -07 — ■05 10 •02 — •23 (09 -79) Azimuth Mark 1 10 31 05 01 •90 •85 Cahas 127 24 +0 -04 24-89 + 1 -48 (26-37) Flat Top 138 23 02 •84 +0 •07 02 -91 — -58 (02 -33) Smith Mountain 153 26 57 •69 +0 -04 57 -73 — -68 (57 -05) i Youtig Poore 314 ,354 44 21 12 ■49 -66 -fo -02 12 -51 -71 —0 2 09 +0 ■05 09 +0 01 -go T2-,^3 09-83 ♦Reduction to center — 2"'io, applied. fBuchaiiati, observer. THE MAIN TRIANGULATIOX. 159 Abstracts of horizontal directions at stations comfiositig the second or North Carolina section of the trian}; Illation, i8j6-i8qs — continued. Poore, Wilkes County, North Carolina September 15 to October 11, 1877. 50"" direction theodo- lite No. 3. C. O. Routelle, observer. Auj^ust 30 to September 17, 1895. 45 '•'" direction theoflolite No. 4. A. H. Buchanan, observer. Circle used in XI positions in both years. Corrections Number of directions. ObjeclJ . observed. Result of local adjustment. Approxi- mate probable errors. Reduc- tions to sea level. Resulting seconds. from ad- justment of .second section. Final seconds. / // /> ., // // // Mark 1877 00 00 -00 ±0-07 6 Buffalo i«77. 1895 32 47 15-52 -12 +0 -08 15-60 -0-39 15-21 7 Moore Mark 1877 1895 60 60 05 55 54 ■■13 18-32 -II +0-04 54-47 4-0-02 54-49 8 Young 1877 123 21 iS -64 -16 -02 18 -62 4-0 -18 iS-So Anderson 1877 170 22 26-64 0-28 9 King 1877 '85 26 51 -63 0-13 -j-O -QI 51 -64 -0-15 5' -49 10 Benn 1877, 1895 217 22 12 19 012 + -06 12-25 -0-18 12-07 Mount Mitchell 1877 249 45 OS -56 0-54 II Roan High Bluff 1895 270 23 04-91 — -02 04-89 +0-36 05 -25 12 Rogers 1895 329 46 41 -23 — o-io 41 -13 ^0 -16 41 -29 Probat )le error of a single observation of a direction [D. and R. ) in 1877, c, = --±:o"-jS: in 1S95, VoHnj^, Rowan County, North Carolina. September 22 to November 11, 1S76. 50"" direction theodolite No. 3. C. O. Boutelle, observer. Circle used in XI positions. ±0 -oS 0-19 +0-02 09-38 0-17 0-14 +0-04 18 -23 o-r6 +0-04 38 -32 O -12 0-16 +0-02 5497 o-is o -06 29-26 Probable error of a single observation of a direction [^D. and A'. ), t'l = j=o"- Azimuth Mark 00 00 -oo 16 Buffalo 01 09-36 Mocksville Church 16 37 17-07 17 Moore 16 40 18 -19 13 King 218 37 38 -28 Anderson 237 26 03-64 14 Benn 251 II 54 '95 15 Poore 299 32 29 -32 00 00 +0-64 10 -02 -0-52 IS 75 -I -40 36-92 -1-0 -37 55-34 — 0'12 29-14 i6o THE EASTERN OBLIQUE ARC. Abstracts of horizontal directions at stations composing the second or North Carolina section of the triangidation, iSyd-iSg^ — continued. Benn, Burke and Cleveland Counties, North Carolina. July 25 to August 22,1877. 50"" direction theodolite No. 3. C. O. Boutelle, ob.server. Circle used in XI positions. Number of directions. Objects observed. Results of sta- '^^I'at?'" ZtsXo ^^^'^'''^'^ fron't^lnl F"-J tio„ adjustment, probable 4°'>eVe,. ^-'=°"d-'*- adiustSt. ^^™-'-^- Reference Mark Poore Young Anderson King Thicketty Wofford Paris Hogback Mount Mitchell ( Probable error of a single observation of a direction (/?. and A".), d', = rbi'''"oS. 00 00 'GO ±0 -qS 90 24 53 -48 '21 128 03 37 -66 0-15 139 52 09-17 0-28 191 28 17-42 -16 241 16 29-13 0-35 250 34 52-92 -19 274 57 2738 -20 282 51 27-03 -22 342 18 31 76 0-43 July 13 to August 14, 1895. 45'"' direction theodolite No. 4. used in XI positions. A. H. Buchanan, observer. Circle Mark 1895 00 00 -QO Roan High Bluff 21 02 06-70 -0-13 06-57 Poore 98 00 40 -56 +0 -06 40 -62 Probable error of a single observation of a direction (D. and R.), e^- Consolidated results at Benn. -A"-lo. Mark 1877 00 00 -QO 18 Roan High Bluff 13 26 19 -62 -0-13 19-49 -1-25 18 -24 19 Poore 90 24 53-48 -fo -06 55 -54 +0-18 53 -72 20 Young Anderson 128 139 03 52 37 -66 09-17 +0-01 37-67 -0-81 36-86 King * 191 28 17-42 — -04 17-38 +0-23 Thicketty 241 16 29-13 Wofford 250 34 52-92 Paris 274 57 27-38 Hogback 282 51 27-03 Mount Mitchell 342 18 31-75 *The line Kine to Ben n l)ei ng fixed by the southern section. THE MAIN TRIANGULATION. i6i Abstracts of horizontal directions at stations composing the second or North Caroliiia section of the triangulation , /ii (5)- 1 ■S7( i4)+3-o7{i5)-r2o( i6)-o-49( 18)4-3-22 (19) -2-73(20) -r6i(23)+3-38(24)-r77(25)-o-68(26) + r53(27)-o-85(28) o=+7-8-2-55(i)+2-55(2) + r32(4)+4-o8(6)-4-o8(7)-3-38(9)+3-38(io)-o-34(i3) +0-82(15)— 0-48(17)— 0-41(19)^ 2-80(21) — 2-80(22) Nonnal equations. C, C2 c, C4 C5 C6 C7 C8 C9 Cio C,i Cir Ci, I o=— -10 + -1 — 2 — 2 + 7 '91 + 5-91 - 9-39 2 +0-57 +4 + 2 - 9-81 - 2 -60 + 2-07 3 — I -10 + 6 — 2 — 12-30 + 2 -02 - 3 '07 + 7-'"^S 4 +0-52 + 4 -2 - 4 '95 - 3-22 + 9 '97 5 —4-64 +4 + 2 + 8-23 + 0-86 — 2-46 6 -3 '31 +6 + o'59 + 2-47 + 3 '07 - 7 -82 7 — 92 +6 — 2 - 2-76 - 5 -Si + 2-76 8 -1-36 +6 — 2 + 2-61 9 -3 '64 +6 + 3 '53 - 1-44 - 3 '79 10 II -0-5 -5-9 + 153-25 + 0-74 +68 -74 _ 32-12 15-39 -36-64 -17-67 12 + 1-4 ' + 06-92 + 9-00 13 + 7-8 +87-75 C, = +o-7i9 C== -0-653 C3 = + i -096 C4= + I -080 C5= +0-838 Resulting correlates. Cf. =+0-909 C, =+0-726 Cs =+0-890 C, = + 1-252 C,„ = -0-003 86 Resulting corrections to observed directions. Cii = — o -094 o Ci2 = — o -009 16 C,3 = — o -loi 5 (1) = = -0-185 (8) = = +o-i77 (15) = = —0-121 (22) = =+2-052 (2) +0-II8 (9) —0 -146 (16) +0 -637 (23) -0-875 (3) -0 -633 (10) -0-183 (17) +0-517 (24) -- m (4) —0 -190 (II) +0 -362 (18) -I -248 (25) + 1 -268 (5) +0 745 (12) +0 -164 (19) +0 -184 (26) —0 -720 (6) -0 -391 (13) -I -403 (20) -0-813 (27) -0-178 (7) +0-017 (14) +0 -370 (21) -0 -297 (28) +0 -898 Probable error of an observed direction, o"674 /i4-66 zfcO 72. THK MAIN TRIANGULATION. 163 Resulling angles and sides of l/ic second or North Carolina section of the triang illation. No. Stations. Poore Buffalo Moore Young Buffalo Moore Poore Buffalo Young Poore Moore Young Rogers Buffalo Poore Roan High Bluff Rogers Poore Benn Roan High Bluff Poore King Poore Young Benn Poore Young Benn Poore King Benn Young King Observed angles. Correc- tion. Spher- ical aiiKlcs. Spher- ical excess. I,of(. dis- tances. Distances in meters. / // // // // 27 18 38 -87 H 0-41 39 -28 3-51 4-676 356 4 47 463-13 57 5S 31 '49 —0 -19 31 -30 3-51 4-943 028 7 87 7.J5 -87 94 42 60 'oS - -12 59-96 3-52 5 -013 257 103 CJ99-6 16 39 08-85 0-12 08-73 2-31 4-676 356 4 47 463-13 29 01 01 '37 -0-63 00-74 2-31 4-904 942 5 80 34' -98 134 19 57-28 -f6-i8 57-46 2-31 5-073 639 3 118 478 -4 90 34 03 -02 +0-57 03-59 5 -01 5-073 639 3 118 478 4 28 57 30-12 + 0-44 30 -56 5-01 4 -758 644 5 57 364 -67 60 28 40 -12 +0 -76 40 -88 5-01 5 -013 257 •03 099 -6 63 15 24-15 +0-16 24-31 3-81 4-904 942 5 80 341-98 39 36 57-20 +0 -30 57 -50 3-8' 4 -758 644 6 57 364 -69 77 07 48-97 + 0-64 49-61 3-80 4-943 028 8 87 705 -89 72 05 49-12 +0-54 49-66 5-94 5 -013 257 '03 099 -6 44 53 53-33 +0-93 54-26 5 -95 4 -883 517 2 76 474 -60 63 00 34-47 -0-55 33-92 5-95 4 -984 727 I 96 544 -40 52 37 00 -09 +0 -48 00-57 4-97 4 -883 5'7 2 76 474-60 67 59 37 -23 ^- 1 -08 38 -3 > 4-98 4-950 523 6 89 232 -62 59 23 36 -24 — 0-20 36-04 4-97 4-918 217 4 82 835 -67 76 58 34-05 + 1-43 35 -48 4-23 4-950 523 6 89 232 -62 50 00 42 -38 + 1 -66 44-04 4-24 4-846 167 I 70 172 52 53 00 52-64 +0-55 53-19 4-24 4 -864 269 I 73 159-22 36 59 44-86 + 2-35 47-21 4-04 4 -758 644 5 57 364 -67 62 05 33-02 - -0 -32 32-70 4-04 4 -925 530 7 84 242 -39 80 54 50 -94 + 1 -28 52 -22 4-05 4 -973 743 9 94 133 -44 37 3S 44-13 — 1 00 43-13 3 -40 4 -758 644 5 57 364 -67 94 00 53-63 -0-36 53-27 3-40 4-971 70S 3 93 693 -26 48 20 34-29 -0 -49 33-80 3-40 4-846 167 70 172-51 lOI 03 24-07 -0-18 23-89 2-95 4-973 743 9 94 133 -44 31 55 20 -61 —0 -04 20-57 2 96 4-705 136 5 50 715 -oi 47 01 24-71 —0 -30 24-41 2-96 4 -846 167 I 70 172 -52 63 24 39 -94 +0-82 40 -76 3 -60 4-925 530 7 84 242 -39 32 34 16-65 + 1-77 18 -42 3 -60 4 -705 136 7 50 7 '5 03 84 01 09 57 + 2 -05 II 62 3 -60 4-971 70S 5 93 693 30 164 THE EASTERN OBLIQUE ARC. No. 25. King WoffbrdSl Hogback iParis JPirmacl Mduldin ^-V^ iRabi "'4. Currcthec {Skitt \Blood Grass Sat Kilometer s o 10 20 Statute Miles 6. THIRD OR SOUTH CAROLINA SECTION OF THE TRI- ANGULATION SOUTH OF THE TRANSCONTINENTAL TRIANGULATION, 1873-1877. This section completes the connection of the Kent Island and Atlanta bases, as already indicated in the preceding sec- tion. The results of the adjustment made in Octol)er, 1878, are retained, omitting only the two quadrilaterals lying be- tween the stations Butt'alo and King, which were included in the second section. The conditional equations, as well as the normal equations, are presented in full, leaving out the eight triangles between the two stations named above, as they are superseded by the present arrangement. The old, and less convenient, notation of the corrections to the angles has been changed, and the order of the presentation of the triangles has been reversed .so as to proceed from the northeast toward the southwest. The third place of decimals in the seconds of the angles was dropped as unnecessary, particularli' since no corrections for height of .stations ob.served upon were made, the maximum valueof this correction being below o"'i. The .stations involved and their approximate heights are as follows: Hogback Wofford Pinnacle Paris Mauldin Rabun Currahee Blood Skitt Relative weights to the directions were introduced in the same way as had been employed in the adjustnient of the Atlanta Ixa.se net. Referring to the explanation there given, the valueof the mean clo.sing error of a triangle ( derived from 73 cases in the triangulation connecting stations Buf- Meters, Feet. 984-4 3 230 267-6 S7S I 047-4 3 436 626-1 2 054 404 -s I 3 28 I 437-7 4 717 530-2 I 740 T 360-4 4 463 632 -7 2 076 falo, Virginia, and Kenesaw, Georgia ) is 'V^-^'= 73 I '94 :i '94 and the probal)le error of a direction is 0-674 --7^ = dzo"-54 ; also the average probable error of an observed direction (see abstracts) f, = d=o"-i8, hence f/— (0-54 )' — (o- 18 )° = o-255, which was added as a constant to the square of each observ- ing error. We have r- = sJ-\-e; and the weight p—ile'\ in order to make the average weight nearly unity, the reciprocal was divided b>- 0-28. The reciprocal relative weights are tabulated farther on; the minimum value of *' or- iso'5 and the maximum 1-3. * From the 33 triangles directly mvolveil here we ha ■30 and the mean error of a direction becomes ±o"7S. I I THE MAIN TRIANGULATION. l6^ * Abstracts of horizontal directions at stations coniprisint:; the third or South Carolina section of the triajigulation , /i'/j-/.?//. /\!n<^, Gaston County, North Carolina. November 26 to December 30, 1S76, and June 17-25, 1877^ 50<^" direction theodolite No. 3. C. (). HouUlle, observer. Circle used in XI positions. Nuinberof directions. Objcct.s ob.served Azimuth Mark 64 Benn Poore Anderson Young 61 Wofford 62 Paris Thicketty 63 Hogback Mount Mitchell Results of local ad- justnienl. 00 00 'OtK) 1 34 43 "656 4S 36 O.S-3]I 66 5 1 08 -804 85 35 53 '167 284 16 ] S -996 293 54 20 -098 296 01 01 -905 307 36 45 '893 345 51 56-4 -0 '014 ^,.-„, menl of third ±0 '06 O '20 o 16 O '24 0-15 O '12 O tS o -26 016 -0 -444 -I 724 -rO-413 Probable error of a single observation of a direction (D. and R. ), (?(■/(•, Greenville County, South Carolina. August 16 to September i, 1S76. 50"' direction theodo. lite No. 3. C. O. Boutelle, observer. Circle used in XI positions. ±o-oS -21 0-15 -28 -16 + 0-230 17 654 0-35 0-19 + -604 53 -520 0-20 -f 705 28-081 -22 -O-56S 26 -459 0-43 58 Paris 59 Mauldin 60 Pinnacle Mount Mitchell 55 Benn 56 King Thicketty 57 Wofford o 00 00 000 15 44 50-325 46 26 55 '104 158 32 15-94 20S 54 59-171 243 34 02 -348 253 55 03-471 282 16 22 -064 ±0 -07 o -11 o' 17 0-44 0-12 o-i8 0-I4 0-I7 -0-178 59 -822 — -03S 50 -287 +1-278 56 -582 —0-287 5S-SS4 -0 -339 02 009 -0-416 21 -648 Probable error of a single observation of a direction (/). and A\). c-, = zl:o''' -Si. i66 THE EASTERN OBLIQUE ARC. Abstracts of horizontal directious at stations coiiiprising the third or South Carotma section of the triangiilatioii, iSj-;-iSjj -continued. IVojford, Spartanburg County, South Carolina. July 6 to August 7, 1876. 50'^'" direction theodolite No. 3. C. O. Boutelle, observer. Circle used in XI position.s. Numberof directions. Objects Thicketty 54 King 50 Paris 51 Pinnacle 52 Hogback Mount Mitchell 53 Benn Results of local ad- justineut. O 22 226 235 264 300 33S GO '000 08 '507 58 -853 59"i37 27 49 '062 04 42 50 02 -589 '^l„?? meutof third dzO '09 0-I4 o-i6 o '16 o -26 +0 -580 +0 -635 -o -656 +0 -862 0-I5 1-343 Probable error of a .single observation of a direction ( /). and R. ] -±o" 'gS. Final seconds. 09 "087 59 -488 58 -481 49 "924 01 '246 Pinnacle, Pickens County, South Carolina. August 25 to September 8, 1875. 50'"' direction theodo- lite No. 3. C. O. Boutelle, observer. Circle used in XI position,'?. 38 Paris 39 Mauldin 40 Currahee 41 Rabun 36 Hogback 37 Wofford O 00 00 "000 48 46 48 '017 117 37 44 '518 153 07 06 -908 321 u2 43-547 347 34 20 -804 iO 'lo o -17 O •\2 o •14 O '21 o '17 +0 -258 +0 -032 +0 -269 +0 -856 -o -887 --0-637 Probable error of a single observation of a direction [D. and R. ), t'i= ±:o"-92. Paris, Greenville County, South Carolina. September 16 lo November 20, 1875. y^"'' theodolite No. 3. C. O. Boutelle, observer. Circle used in XI positions. 00 -258 48 -049 44 787 07 -764 42 -660 20-167 direction o 00 00 -000 94 35 47 "974 109 45 43 "oSo 1 15 36 49 -945 142 59 15 -298 144 27 28-012 15S 30 21-824 229 12 08-277 30S 16 00-933 314 06 42-296 343 20 09 -423 Probable error of a single observation of a direction {D. and R. ), i'i= ±0^-93. 45 Pinnacle 46 Hogback Propst 47 Beiin Thicketty 48 King 49 Wofford Azimuth Mark 42 Mauldin 43 Currahee 44 Rabun ±0 -06 -0 -079 59 '921 -19 fo -020 47 -994 0-17 0-09 + 1-183 51-128 0-17 -21 --0-I55 27 -857 0-2I +0 -304 22 -128 0-I7 -14 -0-755 ■ 00 - 1 78 0-18 -0 -947 41 -349 0-16 +0 -320 09 743 THE MAIN TRIANGULATION. 167 Abstracts of horizontal direclions at stations comprisinf:; the third or South Carolina section of the trianjj^iilation , 1R73- /Hyy — coiiti iiued . JMatttdin, Pickens County, vSouth Carolina. December S to 14, [875. 50"" direction thecjdolite No .3. C. (). Boutelle, observer. Circle used in XI positions. ,,,•,„ , ^ ,, Results of local ad- '^'''*/'l''A"?'''"' from adjust- Final Objects observed. justment. Trror' ment of third second.s. Number of direction.s. I 33 Pinnacle 34 Hogback 35 Paris 31 Currahee 32 Rabun secliou. / // // n n 00 (XI "CXX) ±0 '07 t-O '022 00 -022 61 33 5' -967 o-i8 -0-598 51 369 79 29 1 2 -823 o-i6 + 1 -215 14 -038 267 13 16-950 -12 -I-0-II2 17-062 307 25 59 -062 Q-II -0 -678 58 -384 Probable error of a single observation of a direction {D. and R. ), ^,= d=o"-77. Ratnm, Rabun County, Georgia. July 27 to August 5, 1875. 50'"' direction theodolite No. 3. C. O. Boutelle, observer. Circle used in XI positions. o / // o 00 00 -(XX) 51 4'^^ 33 '214 80 53 21 -496 89 5' 56-194 no 31 24-370 304 59 5>'^'ii9 315 13 "1 "555 32S 05 38 -177 Probable error of a single observation of a direction ( P. and R Currahee, Habersham Count}-, Georgia. September 17 to November 21, 1874. 50'"' direction theod- olite No. 3. C. O. Boutelle, observer. Circle used in XI positions. Walhalla 28 Currahee 29 vSkitt Yonah 3" Blood 25 Pinnacle 26 Paris 27 Mauldin ±0 -08 -20 -0-351 32-863 0-17 -f I -023 22-519 0-23 0-31 -0 -354 24-016 0-15 —0 -987 57 •132 - r 2 —0 -220 01 -535 0-14 -0 -S30 39-007 .), i\ = ±0^-85. ► Azimuth Mark 22 Pinnacle 23 Paris 24 Mauldin 18 Sawnt^ 19 Skitt Yonah 20 Blood 21 Rabun O 00 CX) -QOO 9 3> 57 '621 26 01 CX3-177 27 54 22 -374 209 40 29 -255 229 04 06 -507 254 59 47 703 255 14 09-621 331 49 ,So-24S ±0-07 o -11 0-I4 0-14 0-14 o -16 0-25 0-I5 0-17 —0 -042 57 -579 +0 -0S5 00-262 +0 -369 22 -743 -0 -552 28 -703 -0-432 06 075 +0 -661 — o -090 10-2S2 50-158 Probable error of a single observation of a direction ( /•>. and A'. ), ^, = =t o"-So. i68 I THE EASTERN OBLIQUE ARC. Abslracts of horizontal directions at stations comprising the third or South Carolina section of the triangulation, i8jj-i8jj — continued. Blood, Union County, Georgia. June 30 to July 15, 1S75. 50'^™ direction theodolite No. 3. C. O. Boutelle, observer. Circle used in XI positions. Corrections Number of directions. ( Yonah 15 Skitt 16 Sawnee 17 Grassy Cohutta 13 Rabun 14 Currahee Objects observed. justment. O GO 00 '000 23 53 12-312 Si 25 II -718 113 23 06 •2S0 167 15 34 '393 307 42 15 -079 355 23 50 761 Probable error of a single observation of a direction ( /). and R. \ Skitt, White County, Georgia. August 14 to 25, 1S74. 50'™ direction theodolite No. 3. C. O. Boutelle, observer. Circle used in XI positions. probable error. from adjust- ment of third section. Final seconds. // // // ±0 -qS 0-I7 -0 -403 II -909 '19 +0 -383 12 -lOI 0-22 +0 •480 06 -760 o-!9 0-I4 —0 '221 14 -858 0-I5 -0-195 50 -566 e.),^.= ±o"-94. Yonah II Rabun 12 Currahee 8 Sawnee 9 Grassy 10 Blood 00 GO -000 zbo -09 33 56 23-941 -16 -0-105 23 -836 82 05 53 '452 0-15 -(-0-510 53 '962 230 31 07 -207 0-17 —0-009 07-198 264 50 54 -066 -14 —( -304 53 762 319 45 17-372 0-I5 —0 -092 17 -280 Probable error of a single observation of a direction (£>. and J?.), t',= ,rb o"-84. Sawnee, Forsyth County, Georgia. October 7 to November 12, 1873, siif^ November 26 to December 4, 1873. 75"" direction theodolite No. i and 50=" direction theodolite No. 3. C. O. Boutelle, observer. Corrections LlOllb K.CbUlLlU^ from base direc- Tif.t afl- timi+(39)-(33)K34)-(59)+(6o) o=-2-727-(34)-f(35)-(42)4-(46)-(5S) + (59) o=+o-oi3-(37)+(38)-(45) + (49)-(5o) + (5i) o=-3-463-(57) + (6o)- (36)-| (37) - (5' ) + (52) 0= -0750- (57)+ (58) (46)-(49)-(5o) + (52) o= + 2755-(47) + (49)- (50) + (53)-(66) t (67) o=+3-5o6- (55)+(57)-{52)n (53)-(66) + (6S) o=-2-i24-(56) + (58)--(46) + (48)~(62) + (63) o=4o-390-(56) + (57)^(52) + (54)-(6r)-f(63) o=-i-867-(65) + {66)-(53)+(54)--(6i)-f (64) o=+o-8o5-(7i) + (65)-(64) + (69)-(8i)^(S2) o= + 2-397-(8o) + (82)-(7i) + (72)~(74)+(75) o=-3-26o-(8o) + (8i)-(69)+(7o)-(73)+(75) o=-ro4i-(79) + (So)-(75) + (77)-(83) + (84) o=+o-8o2-(86) + (88)-(78)H-{79)-(84) + (85) o=+o-905-(86) + (87)-(76) + (77)-(83) + (85) o=-o-oi -0-153(1) -0-026(3) -(-o-i79( 2) -o'3o8 (8) +0-456(9) -0-148 (10 1^0-337(16) -o-335(i7)-o-oo2(i5) o=+o-5o+ 1 -295(3) --0-321 (2)-o-974(4)-o-i34( 16) 4-0-521 ( 15 )-o-3S7(i4)-o-598(iS) + 0-975(19) -0-377(20) o=- 1 -53-0-336 (15) +0-387(14) -0-05 1 (13) -0-425 (19) -.-0-377(20)— 0-048(21) +o-749( 29) -0-370(30) -o-379( 28) o=+o-65+o- 142(21) ^0-634(22) +0-492(24) + 0-024(28) -0-945(27)^0-921(26) -0-082(40) + 0-266(39) -0-184(38) I 0-300(44) -o- 166(45) -0-134(42) o= + 2-i2-o-634(22)-5-749(24)46-383(23) -0-082(40) . o-266(39)-o-i84(38) 4 2-o57(43)-o-i66(45) 1-891(42) 0=40-46+0-675(25) I 0-493(27) i-i68(26)+o-i62(32)-o-2oi(33)- 0-039(35) 0-703(44) fo-537(45) r 0-166(42) N. B. — The 6 equations, XXIII to XX\'III, refer to the 2 quadrilaterals iu the old work, of which no further use is made here. The nuniViered corrections are as follows: at AY//", Poore (691, Vouiiji (70); at Beun, Poore (71), Young (72); at }'o/ini;. King (73), Henn (74), Poore (75), Huflfalo (76), Moore (77); at Poore, Buffalo (78), Moore (79), Young (80), King (Si), Benn (82); at Moore, Young (83), Poore (84), Buffalo (85); and at Hiiff'alo, Moore (86), Young (87), and Poore (S8). I/O XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI THE EASTERN OBLIQUE ARC. Observation equations — continued. o=:-o-98+o-i84(39)-o'445(38)+o-26i(36) +0-039(33) -o-6i2(35)-o-65i (34) +0-200(60) -0747(59) +0-547(58) o=+2-6o— 0-694(38) -0-26 r(36)+o-955(37) -0-200(60) -^0-246(58) -0-046(57) + '■319(51)-! '053 (50) -0-266(52) o=-2-34-o-445(46) -0-103(49) +0-548(47) -o-266(5o)+o-325(52) -0-059(53) + i-5iS(67)-i-i84(68)-o-334(66) o= + 2-i7-o-o74(46)— 0-103(49) +0-177(48)— o-266(5o)+o-325(52)— 0-059(53) +0-339(68) -0-334(66) ~o-oo5(65)+o-863(62)-i-oi7(63)+o-i54(64) o=+3"o5— 0-103(46)— 0-738(49) +0-841 (48)— 0-046(58) +0-309(57)— 0-263(56) + i-24o(62)-o-488(63)-o-752(6i) o=— 0-78-0- 174(64) +0-196(69)— 0-022(70)— 0-353(82)^-0-338(81) +0-015(80) +0-516(74) -0-329(73) -0-187 (75) o=+o-20-o-i07(8o) -0-408(78) +o-5i5( 79) -o-o48( 75) +o-704( 76) -o-656( 77) -o-i32(88)+o-379(87)-o-247(86) The last two equations refer to the quadrilaterals already disposed of. Normal equations. C2 C3 C4 C5 C6 C7 Cs C9 Cio Ci, Ci C13 C14 C15 Ci 0=4-1-938 o=— 2-247 0=^3-964 = -0-535 o = +o-73i o=+o 727 0= + 1-572 o= — I -270 o= + t -512 o=-o'559 0= I -311 o=-i-i95 o= — I -616 o=— 2-727 H5-3 +1 -2 + 5-2 +2- +6- +6- + 2-1 +64 +6-2 +2-2 +6-2 Ci= C16 +6-0 +2 —2 +2 + 5-9 +2 +2 +2 +5-9 +2 +6-0 -2 +6 Normal equatioiis—conXxwA^Ci. C18 Cr<) Cso C21 C22 C25 +2 +6 -2 +5-9 C25 C26 -1-9 C23 15 o=+o -0]3 + 5-9 — 2 + 2-r + 2-1 16 o=-3'463 + 6-2 + 2-1 2 ■ 1 2-1 17 0= -0-750 +6-1 + 2-1 -2 -I + ■■9 -2-1 18 o= + 2-755 + 6-1 + 2 -2 19 o = + 3-5o6 +6-2 + 2-1 — 2 20 o= — 2-124 + 6-0 + 2 .... 21 0= +0-390 +6-1 + 2 22 o= — I -867 + 6-1 -2 -I 23 0= +0-805 + 6-2 + 2-1 — 2 24 o= + 2-397 +6-1 + 2 -2 25 o = — 3-260 +6 — 2 36 = — I -04 ! +6 — 2 +2 27 0= +0-802 +6-2 + 2-2 28 0= +0-905 +6-4 THE MAIN TRIANGULATION. 171 C29 C3t Noniia/ equations — com plclec' C32 C33 C34 C35 C36 Cj3 Cji I +0 8067 + 1 •6835 , 2 — 4321 — ■2191 3 — 9705 — ■5210 +0 ■3360 4 +0 1401 -0 •2443 — '0100 5 6 •2742 ■1819 •0100 ■4250 '0440 — +0 + •ilSo 7 +0 1460 +0 •5210 - 1 •4780 8 ^0 ■4270 — ■5700 -o'5520 — 6750 9 -0 •4270 + 1 •3190 -57490 — 3472 +0 77S0 •739" -5 '4630 + 4 '3260 1809 1489 II — •4270 — + 4650 12 +0 ■6260 -8-1840 — 1270 +0 6120 13 + •2660 + o'266o + l8oq + 1578 +0-0871 14 + •1340 + 1 '8910 — 1270 +0 -0237 -02214 -0-4450 —0 -0740 — 00616 Normal equations. — completed. C35 C36 C37 C38 C3') C4 15 -0-0162 — 0-0162 -0 -4833 —0 -4005 +0-7924 +0-1527 +0-1527 -o-8n8 16 —0-0871 -0-5235 +0-3575 +0-3575 -0-3090 17 +0 -4923 + 1-0278 +0 -9552 +0-5842 -1-0592 • 18 + 1 '0530 + 1 -6043 +o'4277 -o-SiiS 19 +0 -2466 - 1 '3849 +0-2904 +0-3090 20 +0 -4923 +0-2214 +0 -4450 -1-6113 -0 -4783 21 +0 -2466 -0"3575 -1-3745 +0 -8360 22 -0-2750 —0-1006 +0-7520 -0-1914 23 -0-1744 -0-3036 24 — I -0710 +0 0590 25 +0 -2470 +0 -0590 26 +0-2020 - 1 -2300 27 + 1-0627 28 -0 6335 Normal eguatioji'^ — completed. C29 C,r C35 C36 C33 C40 29 o=— o'oi +0-6096 -0-1532 +0-0007 30 o=+o-50 +52265 -0-8813 31 o = -i-53 +1-4592 -0-0023 32 o=+o-65 +2-6467 -2-0404 -1-8550 +0-1226 +0-II49 33 o = + 2-i2 +S2-1355 -0-3941 +0-1226 +0-II49 34 o=+o-46 +2-9057 +0-016S 35 o=-o-98 +1-9540 +0-2S41 -0-0226 36 o= + 2-6o +4-4434 +0-1S50 +0-1S50 -00244 37 o=-2-34 +4-8588 -0-0949 +0-1295 38 o= + 2-i7 +2-2S52 +1 -8214 -ooi<)5 39 o=+3-05 +3-8955 40 o=-o-7S +0-7207+00074 41 o = +o-2o +r62S3 1/2 THE EASTERN OBLIQUE ARC. Resnltiuo; I'alues of correlates. C, C. C3 C4 Cs C6 Cs C9 C.o = f I =+0 = — o =+0 = — o = i-o = — o =+I •330 62 ■137 00 •200 89 •694 67 ■510 27 ■263 S3 •105 40 •S55 96 •722 30 •099 17 C„ = C.3 = C.4 = C,6 = C,8 = C,9 = : +0-248 30 :-o'488 74 ^ + 1 '13' 56 ^ + 1 "433 16 : +0-036 14 :— 0-057 86 :+0-223 61 -0-795 56 : + 0-286 98 : + O -840 26 C,i = -o-i42 55 0^,= +0-723 09 C23= +0-957 84 C.4=--i -151 53 C.5= + i -412 85 C,6= +0-424 81 C=7 = +0-139 80 C^8=— 0-302 7 C25=+2 -692 01 C3„=+o-6i4 15 C3i = +I -33" — O C34=-0 C35=+0 €36= "O C37 = +0 C,8=+0 C3,= -I C40=-0 C4i = -o ■224 74 ■214 82 ■102 086 ■193 85 ■454 91 ■56S 89 •946 19 ■934 10 ■362 70 ■598 29 016 91 (I) (2) (3) (4) (5) (6) (7) (8) (9) (10) (II) (>2) (13) (14) (15) (i6) (17) (18) (19) (20) (21) (22) 0-5 I -I I '3 I -r I -o I -o 0-5 I -o I -o I -o I o I -o I -o I -o I -o I -o I -I I -o I -o I -o I -o I -o Reciprocals of weights and resulting corrections to observed directions. I — o -1091 +0 -7998 -0-1235 -o -4552 -I '3379 + 1 "5315 — o -0968 — o -0088 -o -3040 — o -092 1 -0-1054 -f 0-5103 — o 2209 -o -1946 — o -4032 +0 -3826 +0 -4797 -0-5517 -o -4320 +0 -6610 — o -0898 — o -0423 (23 (24 (25 (26 (27 (28 (29 (30 (31 (32 (33 (34 (35 (36 (37 (38 (39 (40 (41 (42 (43 (44 P I -o I -o I -o I -o I -o I o I -o I -2 I -o 0-9 0-9 ( I -o I -o I -I I -o 0-9 I -o I -o I o I -o I -o I -Q -t-o -0854 +0 -3693 -o -9868 — o -2197 +0 -8298 -0-3512 + 1 -0227 -o 3537 +0 -1119 -o -6783 4 o -0219 -o -5978 + 1 '2153 -0-887I - o -6373 +0-2581 +0-0318 +0 -2692 +0 -8560 -o -7548 — o -9470 +0 -3201 (45 (46 (47 (48 (49 (50 (51 (52 (53 (54 (55 (56 (57 (58 (59 (60 (61 (62 (63 (64 (65 (66 J 0-9 I -o 0-9 I -I 0-9 I -o r -o r T I -Q I -o I -o I -o I -o 0-9 I -o I -o I -o I -o I -o I -o I -o I -o — o -0789 +0 -0195 +1 -1827 -0-1545 +0 -3038 +0 -6347 - o -6564 +0 -8621 - 1 '3426 +0 -5805 — o -2870 -o -3393 —0-4162 — o -1780 — o -0382 +1-2785 +0 -4442 -I 7239 +0-4127 +0 -0145 +0 -2301 +0 -6036 (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78) (79) (80) (81) (82) (83) (84) (85) (86) (87) (88) — V -I +0 -7048 -I -0 -5683 -0 —0-5722 -0 + 1 -4260 -I +0-2130 -0 -I '1515 -0 — I -2160 -0 + -8429 -0 — -0508 ■0 +0 -2908 -0 +0-1331 •0 —0-1329 •0 -0 -2938 -0 +0-1564 •0 +0 -2528 -0 + 0-0175 •0 —0 -1220 •Q +0 -2850 •I -0 -3089 •I +0-1893 -2 — 0-371 1 -0 +O-I42I THR MAIN TRIANGULATION. ^73 A'fsu//h/i^r angles and sides of tlw third or South Carolina section of the triangnlalion. No. Wofford Beim King Hogback Beiiii King Paris Benn King Wofford Hogback King Hogback Benn Wofford Paris King Wofford Paris Hogback Benn Paris Hogback King Paris Benn Wofford Paris Hogback Wofford Pinnacle Hogback Paris Pinnacle Hogback Wofford Observed .angles. Correc- tion. Spher- ical angles. Spher •cal exces.s / // // // // 43 35 05-92 + 1 -92 07 -84 2-64 .59 06 35 '49 fo38 35 -87 2-65 77 18 24 -66 -0-43 24-23 2-65 34 39 03-18 -0-05 03-13 3-10 91 23 09 '60 -o-8o 08 80 3-09 53 57 57l(> —0 -40 57 -36 3-10 28 50 3S -07 -1-34 36-73 4-15 83 29 09-95 -1-0 -47 10 42 4-15 67 40 23 -56 + 1-74 25 -30 4-15 117 57 19-44 -0 -2S 19 -16 1-89 3'S 42 19-72 --0 -08 19-64 1-89 23 20 26 -90 -0-03 26 -87 I -89 73 21 22 -89 -0-13 22 -76 2-34 32 16 34-11 -I -■■7 32 94 2-34 74 22 13-53 — 2 -21 II -32 2 '34 14 02 53 -Si + 0-46 54-27 0-93 9 37 61 -lo -2-17 58-93 0-94 156 19 09-65 -0-05 09 -60 0-93 21 01 01 -97 + \ -16 03-13 0-82 151 05 00-83 -j-O -II 00 -94 o-Si 7 53 59-65 -I -27 58 -38 -82 49 5' 40-04 — o-iS 39-85 I -87 116 25 57-65 +0-16 57-81 1-87 13 42 25 -So +2-14 27-94 1-87 42 53 31 -88 -0 -88 31 -00 2-44 24 22 34-46 + 0-I0 34-56 2-44 \\2 44 03-74 — I -98 01 -76 2-44 63 54 33 -85 +0 -28 34-13 -92 77 43 37 -94 +0-24 38-18 -92 3^^ 21 50-21 + 0-23 50 -44 -91 3S 57 16-45 + I-I5 17 -60 0-74 46 26 55-10 -^i -46 56-56 0-75 94 35 47-97 —0 'lO 48 -07 0-74 26 31 37 -26 +0-25 37-51 1 '23 124 10 33 -04 + 1 -70 34 -74 I -23 29 17 49-92 + 1 -52 51 -44 I -23 I-og. distances. 4-705 4 -800 4-855 4 -705 4-950 4 -858 4-705 5-018 4-9S7 4 950 4-800 4 -602 4 -855 4 -602 4-858 4 -800 4-638 5-018 4 -858 4-987 4-441 4-950 5 -018 4-441 4 -S55 4 -638 4 -987 4 -602 4 -638 4-441 4 441 4-503 4-641 4-602 4-869 4-641 .'36 6 210 3 9(ji 2 136 6 231 9 124 o 136 6 914 I 882 5 231 9 210 3 019 6 901 2 019 6 124 I 210 3 655 1 914 I 124 o 8S2 4 543 7 231 S 914 o 543 7 901 2 655 1 8S2 5 019 5 655 o 543 7 543 9 290 4 697 6 019 6 757 3 697 5 Distances in meters. 50 715 02 63 I 26 -29 71 763 10 50 715 -02 89 172-70 72 131 -33 50 715-02 104 451 -4 97 248-41 89 172 -70 63 126 29 39 996 -28 71 763-10 39 996 -28 72 131 -35 63 126-29 43 516-62 104 451 -4 72 :3i '33 97 24S-39 27 640 -36 89 172 -67 104 451 -4 27 640 -36 71 763-10 43 516 62 97 248-41 39 996 27 45 516-61 27 640-36 27 640-37 31 863 27 43 S22 -55 39 996 -28 74 0S9 -61 43 822 -53 174 Ixesnliiug angles and sides THE EASTERN OBLIQUE ARC. 13 14 15 16 17 iS 19 Pinnacle Wofford Paris Mauldin Hogback Paris Mauldin Pinnacle Hogback Mauldin Pinnacle Paris Rabun Pinnacle Paris Rabun Paris Mauldin Rabun Pinnacle Mauldin Currahee Pinnacle Paris f Cur \ Pin urrahee nacle IMauldin 2i Currahee Paris Mauldin Currahee Rabun Pinnacle Currahee Rabun Paris he 1/ u-d or Soitt/i Carolina section of the tr iangulation — continued. observed angles. Correct- tion. Spher- ical angles. Spher- ical excess. Log. distances. Di.stances in meters. / n // // // 12 25 39 '20 +0-90 40 -10 0-43 4 -638 655 I 43 516-62 9 03 60-28 -1-29 58-99 0-43 4 -503 290 4 3' 863 -27 15S 30 21 -82 +0-38 22 -20 0-43 4 -869 757 3 74 0S9 -61 17 55 20 -86 + 1 -81 22 -67 0-31 4-441 543 5 27 640 -35 15 44 50 -32 +0-14 50-46 -32 4 -386 965 5 24 376-17 146 '9 47-04 +0-78 47 -'^2 0-32 4-697 196 I 49 796-18 61 33 51 '97 -0 -62 51 -35 0-94 4-641 697 4 43 822 -52 87 44 04-47 +0 -92 05-39 0-94 4-697 196 3 49 796-21 30 42 04 -78 + 1 -31 06 -09 0-95 4 -405 586 3 25 444 -05 79 29 12-82 ^-I -19 14 -01 0-52 4 -503 290 3 31 863 -26 48 46 48 -02 -^-0 -23 47-79 0-52 4 -386 965 6 24 376-18 51 43 59 '07 +0-68 59 -75 0-51 4 -405 586 3 25 444 -05 10 13 03 '44 +0-76 04 -20 0-63 4-503 290 7 31 863 -29 153 07 06-91 +0-60 07-51 0-63 4-909 644 5 81 216-55 16 39 50 -58 —0 -40 50-18 0-63 4-711 876 7 51 508 -24 12 52 36 -62 +1 -05 37-67 -96 4 -386 965 4 24 376-17 35 04 08 -49 -fi -08 09 -56 -96 4 -798 27S I 62 846 -08 132 03 1376 _ +1 -90 15-66 0-97 4-909 644 2 81 216 -49 23 05 40 -06 +1-82 41 -88 I -08 4-405 586 5 25 444 -06 104 20 18-89 +0-82 19-71 1 -07 4 -798 278 2 62 846 -09 52 34 00 -94 +0-70 01 -64 f -08 4-711 876 7 51 508 -24 16 29 02-56 +0-13 02 -69 I -93 4-503 290 31 S63 -24 117 37 44-52 +0 -01 44 -53 I -93 4-997 790 99 492 '42 45 53 17 -70 +0 -87 18 -57 1 -93 4 -906 481 9 80 627 -26 IS 22 2475 +0-41 25 -16 I -62 4-405 586 I 25 444 -04 6.S 50 56-50 +0-24 56-74 I -62 4-876 702 I 75 283 -90 92 46 43 '05 —0 -09 42-96 I -62 4 -906 481 9 80 627 -26 ] 53 22 -20 + -29 22-49 -21 4 -386 965 3 24 376-16 5 50 41 '36 —0-19 41 -17 -21 4 -876 702 I 75 283 -90 172 15 55 -87 -^-I "lO 56 -97 -21 4-997 789 9 99 492 -40 37 42 07-37 -fo-05 07-42 2 -04 4-711 876 7 51 508 -24 106 48 35-10 +0-63 35 -73 2-05 4 -906 481 9 80 627 -26 35 29 22-39 +0-59 22 -98 2-04 4 -689 285 I 48 897 -33 54 1 1 09-93 4-0-17 10 -10 3-34 4-909 644 I 81 216-47 96 35 31-66 -0-13 31 -53 3-35 4-997 789 9 99 492 -40 29 13 27-13 +1 -27 28 -40 3-34 4-689 285 I 48 897 -33 Resultmg auf^les i 27 28 29 31 32 33 34 Blood labim Currahee Skitt Rabun Currahee Blood Rabun Skitt Skitt Blood Currahee Sawnee Blood Currahee Sawnee Skitt Currahee Sawnee Blood Skitt Grassy Blood Skitt Grassy Skitt Sawnee Grassy Blood Sawnee PHE , M AIN T] \^^ Johjxa "t Grassy;^ (^Brandon. /Lavender V\GEORGLA^ i^ ^^^^^iPine Log ALABAMAX // \ Sweat Mt. Indian. ' — ^^^^Q^^ Carnes Kencsa-w Kilometers 10 10 20 30 40 50 60 Statute Miles 70 80 90 100 10 10 20 30 40 60 60 This triangulation is located in Georgia and Alabama, and is of the same complex character as the Atlanta ba.se net. It depends for the length of its sides upon the Atlanta base, and on the accompanying sketch is shown, by two heavy lines, the connection with the base net.* The section depends for the length of its sides directly *'rhe computation and adjustment made in 187,5 and retained here has no corrections applied to the directions for height of stations observed. These are too small in comparison with the observing error to require special consideration- In a newcomp\itation it would have sufficed to limit the iecoiuh of the angular directions to two places of decimals. THK MAIN TRIANGULATIOX. 179 ■46. From the approximate probable errors of the observed upon the Atlanta base. It is composed of 22 triangles. The angles were measured by Assistants F. P. Webl)er and C. O. Boutelle, in the j-ears 1^73-74-75, and five different in.struments were employed. Weights to the .several directions were intro- duced in the adjustment, depending in part on the approximate probable errors of the observations at a station and in part on the closing errors of the triangles. We have the mean error of a triangle from the sum of the squares of the closing errors — -x-?-^ — =iti"'69, and that of an angle =±o"'y7; also the probable error of a direc- V 22 I '69 tion =^ o"674 —^ = ±0 directions, as given in the aljstracts of the respective .stations, we have the average value f, = ±o"'i8, hence the .square of the triangle combination error fj= (o'46/ — (o'lS)- = o'i8, and adding this to the square of f,, we have t^— i p — e^^+e^, whence the relative weight p to each direction. We have also the ratio of the greatest to the least weight 2 "53 to i. The approximate heights of the stations above the Atlantic are as follows: Meters. Feet. Carnes 396 9 i 302 Lavender 5i5'2 i 690 Johns 577 •-! I S94 Indian 603-4 I 9S0 Gulf 673-3 2 :>09 Brandon SH'S i 679 Abstracts of horizontal directions at stations coinposiiig tlic first section 2eest of the ^Itlanta base net. Kenesa-iC, Cobb County, Georgia. June 23 to July iS, 1S73. 75"" direction theodolite No. i. F. P. W'ebber, observer. Correclioii.s Kesmiiii^ uiiceiKiiis objects observed. Nuniherof directions. Resulting directions f^^ ^^^j„ t- Final from previous ad- ,„e„t of first seconds. justuient of net. nient ot first i«ction. Sweat Mountain Carnes Lavender Pine Log o 00 00 -049 224 20 15-063 252 07 00 -702 303 37 22-129 -2 019 2 -009 13 "044 02 -711 Pine Log, Bartow County, Georgia. July 29 to September 17, 1S74. 30^'" repeating tlieodolite No. 32. F. P. Webber, ob.server. ; 2 Carnes 3 Indian Coosa 4 Lavender 5 Gulf Point 6 Johns Cohutta Gra.ssy Sweat Mountain Kenesaw 00 oo-ooo — •710 59 ■290 22 30 3^ '597 -t-i •030 39 •627 ",6 1 7 34 '507 46 2S -f •225 •35 '753 7« >9 50 -280 -i •251 50 ■531 84 39 43 •143 -^ ■471 43 -614 141 193 2S5 ■;o8 29 10 12-849 39 "409 1 • 339 39-128 correction 19 ;eau ^ - 253 I So THE EASTERN OBLIQUE ARC. Abstracts of horizontal directions at stations composing the first section west of the Atlanta base net, /S^j-iSy^ — continued. Sweat Mountain, Cobb County, Georgia. No. I. Number of directions. Objects observed. September lo to October 3, 1873. F. P. Webber, observer. Resulting directions from previous ad- justment of net. 75^™ direction theodolite Corrections from adjust- ment of first section. Final seconds. Kene.saw Carnes Pine Log Grassy o 32 100 145 00 00 '016 34 43 '017 54 55 "552 16 24 -564 -o '203 42 -814 Grassy, Pickens County, Georgia. July 13 to 28, 1874. ^o"" direction theodolite No. 3. C. O. Boutelle, observer. 00 GO '228 43 29 35 '930 51 39 31 -927 86 41 37 784 131 59 17 -061 183 15 38 -93 261 37 28 -06 297 13 10-62 Sawnee Sweat Mountain Kene.saw Pine Log Johns Cohutta Blood Skitt Carnes, Polk County, Georgia. November 17 to December 27, 1873 No. 32. F. P. Webber, observer. ^ J Results from local ' ■ adjustment. O 00 00 '000 7 04 48-139 183 44 53 '383 230 04 00 -691 232 44 12-747 310 57 24-950 317 59 30-451 348 14 27 -327 -2-193 14 -868 30"" repeating theodolite Number of directions. Objects ol 14 Kenesaw Lost Mountain 10 Indian Coosa II Lavender 12 Pine Log Pine Mountain 13 Sweat Mountain jproximat probable error. ; Corrections from adjustment of first section. // // ito-io -0 -456 0-14 0-I2 -I '345 o-i6 0-I2 -|-o -920 o-jo -0 -045 0-14 -12 +0 -934 Final seconds. 59 '544 52 -038 13 -667 24-905 28 -261 Mean correction — o -002 THE MAIN TRIANGULATION. l8l Abstracts of horizontal directions at stations composing the first section 7vest of the Attanta base net, 1873-1875 — continued. Lavituder, Floyd County, Georgia. October 12, 1874, to January 30, 1875, and August 6 to 12, 1875. jQriii repeating theodolite No. 32. F. V. Webber, ob.server. Number of directions. Ol)jects olwerveil 19 Pine Log Pine Mountain 20 Kenesaw 21 Carnes Coosa, mark 15 Indian Weisner 16 Brandon 17 Gulf Point 18 Johns Cohutta Results from local adju.stment. o / // O GO 00 "GOO 17 49 59 ''SS 30 20 51 -197 55 18 18-473 63 25 38-315 III 29 54 716 137 35 38 -33 189 35 31 -660 244 10 24 -069 297 42 46 -291 316 04 49 "376 Approximate Corrections probable from adjustment error. // ±0 -07 o-i6 O'll Q-IO o -09 o -09 0-32 o-o8 o-oS o "II O '12 of first section. H-o -324 Final seconds. Of J -324 — I -058 — o -267 +0 '234 +0-171 +0 -673 — o 'loS 50 139 18 -206 54 950 3' •«3i 24-742 46-183 Mean correction — o -004 /o//;/5. Walker County, Georgia. May 12 to June 21,1875. 30™ direction theodolite No. 107. F. P. Webber, observer. Circle used in XXI positions. 26 Gulf Point Pigeon High Point Cohutta 22 Grassy 23 Pine Log 24 Indian 25 Lavender o 17 44 145 191 00 00 -ooo 13 25 -438 15 12-782 15 56-8 23 00-153 217 34 29-722 294 07 26 -733 297 06 13-557 zbo "lo 0-31 O '20 +0-394 0-20 0-24 o-i6 o -20 — I -240 -^o -672 -ro -247 — I -102 00-394 58-9'3 30-394 26-980 13 455 Mean correction — o -006 Indian, Cherokee County, Alabama. July 24 to August 21, 1875. 30™' direction theodolite No. loS. F. P. Webber, observer. Circle used in XVII positions. 29 Lavender 30 Johns Cohutta Coosa 31 Pine Log 32 Kenesaw 33 Carnes Cheehahaw * Aurora 27 Brandon 28 Gulf Point 00 00 -QOO ±0-06 -0 -244 59 756 3 14 05 -050 0-17 —0-176 04 -874 15 28 22-9 16 44 04 -052 0-22 44 32 I I -956 0-15 ^i -991 13 "947 72 53 48-127 0-12 +0-729 48 -856 74 49 05 -144 0-15 —0 -504 04-640 1S9 16 07 -563 259 21 48 -653 0-I2 301 16 21 -883 o-i6 -0 397 21 -4S6 335 22 53 '053 o"i5 ^Nlean correction -I -41S 51 -635 —0 -i.x-1^ * Observed December 3 to 19, 1885, by O. H. Tittmatm, with sot™ directiou theodolite No. 114. l82 THE EASTERN OBLIQUE ARC. Absiiacts of horizonlal directions at stations ioniposiug the first section zvcst of the Attanta txise net, jS/j-/S/j — continued. Gut/' Point, WaWcer County, Georgia. Septemlier 14 toOctoberg, 1S75. 30'"' ilirection theodolite No. 108. F. P. Webber, F. D. Granger, and J. H. Christian, observers. Circle used in XVII positions. Number of directions. Obje High Point Pigeon Cohutta 34 Johns 35 Pine Log 36 Lavender 37 Indian 38 Brandon Gunter Objects obser\'ed. Results from local adjustment. O GO GO 'GOO 28 39 II -071 55 29 34-156 75 49 36 751 99 04 14-149 139 23 30-004 162 05 54 '020 210 oS 59-511 250 G4 42 -408 Approximate Corrections probable from adjustment error. of first section. ±0-08 0-32 o -16 0-25 0-18 G -14 G -20 G -17 0-45 . Mean correction Final seconds. — I •391 +0 •959 — G •138 + -362 + ■054 35 '360 15-1G8 29 -866 54 '382 59 '565 ±0 -II -19 G-36 -0 -338 13-818 0-30 + 0-138 54-576 0-31 +0 -164 43 "165 -21 Brandon, Dekalb County, Alabama. December 6 to 26, 1S75. 30"^"' direction theodolite No. ig8. F. P. Webber, observer. o / // // // // Aurora o 00 00 -qog Gunter 61 36 36 -507 39 Gulf Point 16S 10 14-156 40 Lavender 222 49 54 -438 41 Indian 266 og 43 -goi Weisner 293 13 43-092 Mean correction — o-oii Observation equations. I 0=^0-472- (l)+ (2)-(l2) + (l3) II o=-o-426- (7)+ (i)-(i3)r(i4) III G=+3-i67- (8)+ (4)-(i9)-f(2G) IV G=-3-443-(ii) + (i4)- (7)+ (8)-(2G)+(2i) V ■o=+o-752- (6)4- (9)-(22) + (23) VI o=+o-G95-(i8)+(i9)~ (4)+ (6)-(23)-l (25) VII 0= -0-544- (10) + (12)- (2)+ (3)-(3i) + (33) VIII o=-2-505-(io) + (ii)-(2i)+(i5)-(29)4 (33) IX o=--2-293~ (5)+ (6)-(23) + (26)-(34) + (35) X I o=-2-o34-(28) + (3i)- (3)+ (5)-(35)^ (37) XI G=-3-i44~(28) + (3o)-(24) + (26)-(34)4(37) XII o=-o-i2o-(27) + (29)-(i5)-!-(i6)-(4G) + (4i) XIII G=-^i-i67-(i6)f(i7)-(36) + {38)-(39)+(4o) XIV o=+o-827-{27) + (2S)-(37) + (38)-(39)-| (41) XV 0= + I -382+0-8286 ( 14 ) — I -Gi 14 (13)4-0- 1828( 12)— 0.3295(1) +0-1664 (2) XVI o=+8-o23+6-6oi4( 14) -6-6014(10) -0-0398 (7) + i2-5i7i(33)-i2-8777(32)+G-36o6(3i) -o-6745(2)+o-5o8i(3) THE MAIN TRIANGULATION. 1^3 XVII XVIII XIX XX XXI XXII XXIII o= I 8-667 |-6-6oi4( 14)— 6-6014(10) —(V59_^4{2i) i 0-4524(20) - ()-i4io( r.S) —12-8777 (32) +0-3997(8) -o-3997( 7 ) I 1 2 -8206 (33 ) +0-057 ' ( 29) 0= -t- 1-425 -0-2868(21) f 0-1410(15) -I o. 1458(19) +0-3035(33) -fo-o57i( 29) -0-3606(31) +0-3081 (2) H o-2()tx)(4) -0-5081(3) o=-o-7or-4-oo6i(25)-|-4'045o(24)-o-o389(23) -3-51 15(29) .3-7255(30) -0-2140(31) -I 0-7414(4)^0-2677 (6) -0-4737(3) o= — 1-290-4-1528(25) 14-0450(24) 10-1078(26) 4'i<'^5'>(29) — 3725S(3o)^o-4595(28) -0-6079(36)40-1047(34) ^ 0-5032(37) o=— 0-736+0-2662(18) -0-1556(1 7)— 0-1 106(19 1-0-1047(36) —0-3855 (34) -0-4902(35) -0-2677 (4) -0-5564(6) 1 0-8241 (5 ) o=+o-2i9-o-33i6(29) -I 0-4595(28) -01 279(27) -0-4297(36) +0-5032 (37) -0-0735(38) +o'3737(4o) -0.2244(40-0-1493(39) o= — 1-514-0-1106(18)— 0-3596(20) +0-4702(19) -<>-. and /?. ), e, ±o"-9t positions. Cahaba, Saint Clair County, Alabama. March 8 to 31, 1886. 50'^'" direction theodolitt- N", 1 14 O. H. Tittmann and J. E. McGra^h, ob.servers. 40 'Wornock o 00 00 -co 41 Aurora 65 09 22 -94 42 Cheehahaw 143 03 52 -83 Alpine 171 08 59-72 Laurel 217 19 44-87 Mean correction o oo Probable error of a single observation of a direction ( D. and A". ), ^'i = =bo"-99. Circle u.sed in VII positions. -0-4S 59-52 —0 -69 22-25 + r -16 53 -99 I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII No. THE MAIN TRIANGULATION. Ohscri'atio)! equations. 191 o=--o77+ (6)~(i3)- o=-o-84+(i5) -(14)- o=-i-8H (i6)-(i5)-t o=+o-25 + (24)-(2S) + (i7) -(i6) + (i2)-(io) o= + o-82+(2o)-(i9)- O=+O-02-f-(2l) -(19) - o=-o-23-|-(3o) -(29)+(23)-(2r) + (27) o= + o-29+(34) -(32 t)=— 2\S2 -1(31 ) — (29 o=-2-o5 + (35)-(34)+(25) -(24) + (io) o=-o-64+(39)-(38)+ (7)- (6)+ (2) (3)-- (2) (5) (4) (4) - (3) + (i3) -(.2) i8)-(i6)+(r2)^-(ir) Hi8)-(i7) + (28)--(27) (26) (30-(3o) + (26)-(25) (23)-(22) + (33)-(32) (9) (r) o=-r50+(42)-(4i)+ (8)- (7) + (38)-{37) o=-o78+(4i)-(4o) + (36)-(35)+ (9)" («) o = + i4-o+2-34(2) + 2-5i (5 )H-2- 18 (6) + 1 -49(12) -3-67(13)- 3-18(14) -4-23(15) -I -05(16) o=-f 2-8— i-96(io)H 2-4o( 11)— 0-44(12) — 3-09! 16)^-4-93(17) — 1-84(18)4-0-01(19)— 3-61(20) —3-62(21) o= + i-7-4-S4(2i)-f5-64(22)-o-So(23)-i-o2(29)-!-3-62(3Q)~2-6o(3i)-i-55(32)-4-4o(33) -2-85(34) o= + 2-3-3-34(9)~.-5-74(io) -2-40(11 )-3-6i (20) --9-25(21 ) 5/64(22) -4-4o(33)-^8-o2(34) -3'62(35) o= + i7-4-o-76(i)+3-io(2) + i-oo(3)-i-i4(4) — i-o5(i5)-i-3o( 16) -o-25( i8)-i-22(i9) + 2-94( 20) -I -72(22)- 1-44(33) -K I -S3 (35) -0-39(36) -2-42(37) -.-3-86(38) -I -44(39) -0-97(40) + 1 -42(41) -0-45(42) Normal equations. C5 C6 C^ Cs C9 Cio Cii Cic C,5 Cu C,; C16 Cir Ci3 = - 0-77 - 0-84 - I -Si + 0-25 -(- 0-82 -I- 0'02 - 0-23 + 0-29 - 2-82 - 2-05 - o'64 - I -50 - 0-78 + 1-1 -o + 2-8 + 1-7 -1- 2-3 + 17-4 C-> C3 C4 +4 + 4 -l-fi — 2 + 2 +6 — 2 -1-2 +6 + 3-5' - 4 '90 -t- 0-12 -^ 0-44 + 0-44 — 2 4-6 -2 +6 + 2 + 2 4-6 - 2-65 + 9-54 + 2-01 . — 10 -40 — - 1-96 + - 5 74 4-84 + S-tSS - 7-52 + 2-07 + .24 ■5<^ +6 -2 +6 -2 +6 + 0-16 + 0-2S +61 -32 - 3 90 + 73-17 + + 1 '7-52 - 63 06-66 — iiS + 277 I C, = -^-i -079 C2= J-o -526 C3=+I -076 C4=-f 0-593 Cs = -fo-[25 Co = -1-0 -177 Remit 111;^ eorielatcs. C; =-i-o-i50 Cs =+0-107 0,= 4-0 -361 C,o= -1-0-980 C,, = -f 0-727 C,,=4-i -on — 2 -10 + 0-o-j + 0-21 - i-3'i J- 2 -61 + 097 + 028 + I -S3 — 1-44 + 4-41 + o-i: + 13 06 + 7-04 — i6-a» — I -20 +6o-o^-> C.5 = -*-o •S07 Cu = — -IS7 C.s= -0 0357 C,6= — ■153 c.,= — •06S C.s= — ■340 I 192 THE EASTERN OBLIQUE ARC. Resulting Corrections to oliscrved directions. (I)= = -0-469 (ii) = = -0-048 (21) = = -fo -267 (31) = = +o-866 (2) -I -844 (12) —0 -621 (22) -0-255 (32) —0-231 (3) -0 '337 (13) +0 -683 (23) +0 -633 (33) +0 -477 (4) -to -938 (14) — I -121 (24) -0 -387 (34) —0 -982 (5) +0 -057 (15) -^o -598 (25) +0 -873 (35) —0 -203 (6) ~o -056 (16) — -170 (26) -0 -043 (36) f -940 (7) -0 -284 (17) + -240 (27) —0 -027 (37) -0-188 (8) +0 -204 (18) +0 "453 (28) —0-416 (38) — I -028 (9) +0 -054 (19) +0-113 (29) -0 -355 (39) + 1 -217 (10) -f -067 (20) -0-759 (30) -0-511 (40) (41) (42) -0-477 -0 -687 + 1 -164 Probable error of an observed direction o-6 -V^- io""67. No. ^suiting angles and si des of tht sect md section of the tr iangittati on 'west of the Atlanta t>ase net. stations. Observec angles. Correc- tions. Spheri- cal angles. Spheri- cal excess. Log. dis- tances. Distances in meters. / " // " // Aurora 44 06 15-57 -0-74 14 -83 2 -OO 4-695 837 9 49 640 -70 Brandon 93 59 16 -82 -0-34 16 -48 2 -OO 4-852 202 7 71 154-56 Indian 41 54 32 -84 + 1-85 34 -69 2 -00 4-677 999 5 47 643 -04 Gunter 33 30 43-00 + 1 -72 44-72 I -32 4-573 188 9 37 427 -34 Gulf Point 39 55 42 -81 +0 -06 42 -87 I -32 4 -638 579 6 43 509 -05 Brandon 106 33 37-32 —0-94 36 -38 I -33 4-S12 764 64 977 -65 Gunter 63 32 43-50 -0-77 42-73 I -55 4 677 999 5 47 643 -04 Brandon 61 36 36-51 + 1 -28 37 -79 ' -54 4-670 389 7 46 815-5' Aurora 54 50 42 -Si + 1 -30 44-11 1 -54 4-638 579 6 43 509 -05 Suiiiniit 67 35 20-19 + 0-03 20 -22 I -I I 4-670 389 7 46 815-51 Gunter 34 15 23-52 + 0-41 23-93 I -II 4 -454 925 I 28 505 -27 Aurora 78 09 19 -86 — -69 19-17 I -10 4-695 149 2 49 562 -05 Rowe 59 59 20 -70 -0 -87 19-83 I -28 4-670 389 7 46 815 -5> Gunter 83 07 58-70 +0-62 59 -32 1 -27 4-729 782 6 53 676-31 Aurora 36 52 45 -25 -0 -57 44 -68 I -28 4-511 •49 9 32 445-16 Rowe 90 13 56-25 -fo-i6 56 -4 r I -02 4 -695 149 2 49 562 -05 Gunter _ 48 52 35 -iS + -21 35 -39 ' -03 4-572 115 2 37 334 -92 Suniniit 40 53 31 -67 -0-39 31 -28 I -03 4-5'r 149 9 32 445 -16 Summit 108 28 51-86 -0-36 51 -50 0-S5 4-729 7S2 6 53 676 -31 Rowe 30 14 35 -55 + 1 03 36 -58 0-86 4-454 925 2 28 505 -27 Aurora 41 16 34-61 — 0-T2 34-49 0-S6 4-572 115 I 37 334 -91 Wilson 64 13 43 -61 — -16 43 -45 '89 4-572 115 2 37 334 -92 Rowe 69 12 59 -34 + 0-37 59-71 -89 4-588 392 3 38 760-76 Summit 46 33 19-49 -f -02 19-51 -89 4-478 573 3 30 100-47 THE MAIN TRIANGULATION. 193 No. 14 '5 16 Rcsuliini:; aiiff/cs and sides of the ! tations. Wornock Rowe Summit Wornock Wilson Summit Wilson Rowe Wornock Wornock Rowe Aurora Wornock Sunnnit Aurora Cheehahaw Aurora Indian Cahaba Aurora Cheehahaw Cahaba Wornock Aurora second section of the ti'ianj^ulation l>asc net — continued. west of the Atlanta 4192 — No. 7 — 02 Ob.serv'et angles. Correc- tion. Spher- ical angles. Spher- ical excess. r,oK. dis- tances. Distances in meters. / // // // // 25 34 30 -89 - I -46 29-43 069 4-572 "5 2 37 334 -92 20 29 47-49 - 0-52 46 97 -69 4-481 194 5 30 282 69 133 55 46-57 — -90 45-67 -69 4 -794 398 5 62 287-16 53 38 20 '86 -0-75 20 • 1 1 0-99 4-588 392 3 38 76rj-76 38 59. 15-33 + 1-38 16 -71 0-99 4-481 194 6 30 282 -70 S7 22 27-08 —0-92 26-16 I "OO 4-681 98 1 5 48 aSi -88 103 12 58 -94 -f I -22 60-16 I -20 4-794 398 5 62 287-16 48 43 11-85 + 0-89 12-74 1 -19 4-681 981 5 48 081 -88 28 03 49-97 -to -71 50 -68 I -19 4-478 573 3 30 100-47 55 43 52-46 -0-6S 51-78 2-19 4-729 782 6 53 676-31 50 44 23 -04 fo-50 23-54 2-19 4-701 488 3 50 290 -77 73 ,■^1 51 -36 —0 -lo 51 -26 2 -20 4-794 398 5 62 287 -16 30 09 21 -57 4-0 -78 22-35 0-65 4-454 925 I 28 505 -27 117 35 21 -57 + 1 -26 22-83 0-64 4-701 488 I 50 290 -75 32 15 1675 4-0 -01 16-76 0-65 4-481 194 4 30 282 -69 55 33 33 -64 + 2-24 35 -88 3-97 4-852 202 7 71 154-56 54 20 56-55 -0-23 56-32 3-97 4-845 763 S 70 107-39 70 05 41 -09 -1-37 39-72 3-98 4-9tation . adjustment. -0-57 —0-62 60-29 44 25 repeating theodolite Corrections for third section. Final seconds. o 00 00 -00 ^o -47 79 16 54-51 -0-55 131 56 48 -89 -0-34 1 86 00 40 -66 — o -64 301 54 18-60 —0-04 Horn, Talladega and Clay Counties, Alabama. March 22 to April 5, 1S87. 30"" repeating theodolite No. 16. O. H. Tittmann and J. H. Turner, observers. May 16 to 22, 18SS. Instrument as before. O. H. Tittmann, J. H. Turner and F. W. Perkins, observers. 00-47 55 06 4S-55 40 02 iS-56 I 13 Alpine 14 Cheehahaw 10 Weogufka II Kahatchee 12 Laurel 00 00-00 -0-59 59 '41 94 14 22-53 -fo -03 22-56 260 49 34 -86 -0 -27 34 59 29S 04 03 -82 —0 02 03 -So 527 42 iS-it +0-S4 iS-95 Laurel, Shelby County, Alabama. May it to 28, 1887. 30'"' repeating theodolite No. 16. O. H. Tittmann and J. H. Turner, observers. April 27 to IMay 10, 1S8S. Instrument as before. P. \V. Perkins and W. B. Fairfield, observers. 15 Cahaba 16 Alpine 17 Horn i8 Kahatchee 19 Weogufka Columbiana 20 Jamison 00 00 -oo +0 -65 00-65 79 45 28 -59 +0 -04 28 63 95 31 01 -66 —0-40 01 26 124 56 26-94 -0-33 26-61 147 5>~-^ r6 -93 —0 -06 16 -87 172 5^1 15 95 17S 28 3>^ -93 — o-io 39 03 196 THE EASTERN OBLIQUE ARC. Abstracts of horizontal directions at stations composing the third section of the triangulation west of Atlanta base net, iS86-/Sgo — continued.- Kahatchct Number of directions. 25 21 22 23 24 Talladega County, Alabama. April iS to 2S, 1S87. 30^'" repeating theodolite No. 16. O. H. Tittniann and J. H. Turner, observers. Objects observed. Jamison Columbiana Laurel Alpine Horn Weogufka Results from station adjustment. O 00 00 '00 41 54 02 -20 93 59 09-51 176 08 20-52 214 55 31 '04 320 17 33 -35 Corrections for third section. +0-30 -0-44 — o -04 +0-I8 Final seconds. 09 -81 20 -08 31 -00 33 '53 IVeogiifka, Coosa County, Alabama. May 28 to June 1 and December 5 to 1888 to January 17, 1889. 30"" repeating theodolite No. 16. F. W. Perkins and W. B. Fairfield, observers. Telescope i"''9 above the ground. 28 Kahatchee 29 Horn Wetumpka Wilder 26 Jami.son 27 Laurel 00 00 -co -o-i8 59-82 37 23 29-76 -f-0-20 29-96 164 03 00-15 200 00 45-06 260 22 41 -69 — -12 41 -57 336 43 24-84 +0 -II 24-95 Mean correction o -00 Jamison, Chilton County, Alabama. February i to March 5, 1889, and May 7 to 14, 1S90. 30"" repeating theodolite No. 16. F. W. Perkins and W. B. Fairfield, observers. Telescope 2"''i above the ground. 30 Laurel 31 Kahatchee 32 Weogufka Wilder Perry I II III IV V VI VII VIII IX X XI 00 GO -00 — Q-ig 59-81 32 28 40 -43 -f -10 40-53 73 08 57 -60 +0 09 57-69 151 38 56 '43 231 10 29 -86 Mean correction 0-00 0= — 1-22+ (6) o=-i-o8+(i4)-(i3)+ (7) o=+2-ii+(i6)-(i5)+ (4) Observation equations. 5)+ (3)- (2) (6)+ (2)- (I) (3)+ (5)- (9) o= + i-99+(22)-(2i) + (i8)-(i6)+ (9)^ (8) u= + o-ii + (23)-(22)-f (8)~ (7) + (i3)-(ii) o=-i-55-f (29)-{27)+(i9)-(i7) + (i2)-(io) o=-o-85+(29)-(28) + (24)-(23) + (ii)-(io) o=-i-o3-|-(3i)-(3o) + (2o)-(i8)+(2i)-(25) o=-fo-25+(32)-(3i) + (25)-(24) + (28)-(26) o=-o-67+(32)-(3o) + (2o)-(i9) + (27)-(26) o=-2-7-4.o2(i)+6-9i(2)+5-96(3)-2-o2(4)-3-33(i2)+3-i7(i3)-fo-i6(i4)-o-38(i5) + 7-84(i6)-7-46(i7) THE MAIN TRIANGULATION. Obaervalion equations — continue'l. 197 XII o=-o-4-ri3(rr)-t-3-33( 12) -2-20(13) --5'37( 16) i-7'46( 17) -2-09(18) -o-29( 21) --2-91 (22) -2-62(23) XIII o=+6-o-2-77( 10) i-6-47( I i)-3-7o(r2)-3-73(i7)-i-8-68(i8)-4-95(i9)-4-«9(27) -7-65(28) --2-76(29) XIV o=-3-i-3-39(i8)+4-95(i9)-r-56(2o)-^o-36(26)+4'S9(27)-5-25(2S) -3-31(30)^5-76(31) —2-45(32) Normal equations. No. Ci C2 C3 C4 C5 C6 C7 Ca C, Ci, C,i Ci2 Ci, C14 I 0= — I -22 -f4 — 2 — 2 _ ■95 2 -i-oS +6 — 2 + 7-92 + 2 20 3 + 2-II +6 — 2 + ■24 - 5-37 4 + ■■99 +6 — 2 — 2 - 7 ■84 + 6-48 + 8-68 - 3 39 5 + *II +6 _2 -1- 3 4 ■17 13 6-60 6-47 0.02 6 -1-55 + 6 +2 — 2 + — 4-13 _ + 006 7 -0-85 +6 —2 + I 49 - I-I7 + 525 8 -1-03 +6 —2 + 2 + I 80 - 8-68 -1- 10-90 9 + 0-25 +6 + 2 + 7-65 - 13-82 10 -0-67 +6 + o-o6 — I -12 II -2-7 + 241 94 - 15 -82 + 40-15 12 -0-4 + 121 -48 - 65-60 + 7-09 13 + 60 + 267-03 — n8oo 14 -3'I + 140-17 Resulting correlates. c, =-0 •003 C6= + -727 c„= — •01 15 c. =+0 ■034 C7=- •495 c..= — •03S9 C3 = -0 •645 C8=- -0 -678 C.3 = -fo -0134 C4 =-0 •985 c,=- -0 ■677 Cx4= +0 •01 84 Cs = — •437 C,c=+o •S09 Hesultinff corrections to observed directions. (l) = =+0 -012 ( 9) = = -0-340 (17) = = -0-399 (25) = = — 0001 (2) —0 -042 (10) -0-269 (18) -0 -334 (26) —0-125 (3) +0 -573 (II) -0-015 (19) -0-057 (27) ^o-io6 (4) —0 -622 (12) +0 -845 (20) -i-o -102 (28) — OM76 (5) —0 -642 (13) -0 -593 (21) 4-0 -296 (29) +0195 (6) -0 -037 (14) +0 -032 (22) -0 -435 (30) — 0192 (7) +0-471 (15) +0 -649 (23) -0 -044 (31) +0105 (8) +0 -548 (16) +0-041 (24) — -1S2 (32) +0-087 Probable error of an observed direction o'Gjs r^ — ^ — V 14 ^6. 198 THE EASTERN OBLIQUE ARC. Resulting angles and sides of the third section 0/ the triangulation ivcst of the Atlanta base net. II L 13 stations. Obse rved angles. Correc- tion. Spherical angles. Spherical excess. dista ices. Distances in meters. / // // // // Alpine 115 53 37 -94 -|~o -61 38-55 1-38 4 -S60 804 4 72 577 -90 Cahaba 28 "5 0573 +0-57 06-30 I -37 4-579 566 6 37 981 -02 Cheehahaw 36 01 19-23 +0-04 19-27 I -37 4-676 196 3 47 445 -64 Horn 94 14 22-53 T-o -62 23-15 0-49 4-579 566 6 37 981 -02 Alpine 58 05 41 -40 +0-51 41-91 0-48 4-509 625 5 32 331 -47 Cheehahaw 27 39 56 '44 —0 -05 56-39 -48 4-247 564 17 683 -33 Laurel 79 45 28 -59 —0 -61 27-98 1-14 4-676 196 3 47 445 -64 Cahaba 46 10 45 -15 — I -20 43 -95 1 -13 4-541 410 I 34 786 '45 Alpine 54 03 51 77 -0-30 51-47 1-13 4 -591 4S2 6 39 037 -55 Horn 32 17 41 -89 -I -44 40-45 0-39 4 -541 410 I 34 7S6 -45 Laurel 15 45 33 -07 -0-44 32-63 0-39 4-247 564 17 683 -33 Alpine 131 56 48-89 —0-81 48-08 0-38 4-685 086 5 48 426 -88 Kahatchee 82 09 II -QI -0-73 ID -28 0-59 4-541 410 I 34 786 -45 Laurel 45 10 58 -35 -0 -37 57 -98 0-58 4 -396 361 24 909 -27 Alpine 52 39 54-3S —0 -89 53 -49 0-58 4-445 918 27 920-17 Kahatchee 3S 47 10-52 +0 -39 ID -91 0-37 4-247 564 17 683 -33 Alpine 79 16 54-51 -{-0 -qS 54-59 0-36 4-443 056 7 27 736 -82 Horn 61 55 56-18 -0-58 55 -60 0-37 4 -396 361 24 909 -27 Kahatchee 120 56 21-53 -0 -34 21 -19 0-57 4-685 086 5 48 426 -88 Laurel 29 25 25 -28 +0-07 25-35 0-56 4-443 056 8 27 736 -83 Horn 29 38 14-29 +0-86 15-15 0-56 4-445 918 27 920 -17 Weogufka 60 40 04-92 +0-09 05 -CI I -66 4 -685 086 5 48 426 -88 Laurel 52 27 15 -27 +0-34 15 -61 I -66 4-643 871 6 44 042 -46 Horn 66 52 43 -25 + 1 -12 44-37 1-67 4 -70S 307 5 51 086 -66 Weogufka 37 23 29-76 +0-37 30-13 0-63 4-443 056 7 27 736 -82 Kahatchee 105 22 02-31 +0-23 02-54 0-62 4-643 871 6 44 042 -46 Horn 37 14 28-96 +0-25 29 -21 0-63 4-441 562 6 27 641 -56 Weogufka 23 16 35-16 —0-28 34 -88 0-47 4-445 918 27 920 -17 Laurel 23 01 49-99 +0-28 50-27 0-47 4-441 562 4 27 641 -.55 Kahatchee 133 41 36-16 +0-II 36-27 0-48 4 -708 307 5 51 086 -66 Jamison 32 28 40-43 +0-30 40-73 0-99 4-445 918 27 920-17 Laurel 53 32 II -99 +0-44 12-43 0-99 4 -621 350 2 41 816-74 Kahatchee 93 59 09-51 +0-29 09 '80 0-98 4714 9'5 2 51 869 -88 Jamison 40 40 17-17 —0 -02 17-15 0-63 4-441 562 5 27 641 -55 Kahatchee 39 42 26-65 -o-i8 26-47 0-63 4-432 911 3 27 096 -38 Weogufka 99 37 18-31 —0-05 18-26 0-62 4 -621 350 2 41 816-74 Jamison 73 oS 57-60 +0-28 57-88 I -14 4-708 307 5 51 086 -66 Laurel 30 30 22 -GO +o-i6 22 -16 I -14 4-432 9" 3 27 096 -38 Weogufka 76 20 43-15 -fo-23 43-38 I -14 4-714 915 2 51 869 -88 THE MAIN TRIANGULATION. lo. thp: fourth section of THE TRIANGULATION WEST OF THE ATLANTA BASE NET, ALABAMA, 1888-1895. ' The triaiigulation l)et\veen the preceding terminal line and the southern limiting line, Creagh to Pollard, follows the valleys of the Coosa and Ala- bama rivers. It is abundantly supplied with check lines, making 30 conditions in the adjustment. The linear de- velopment is 209 kilometers (or 130 statute miles). The whole of the scheme lies south of latitude 33° and the natural elevation of all the spurs avail- able for .stations is less than 220 meters (or 722 feet); farther south the ground slopes gradually to the level of the Gulf. The approxi- mate elevations of the stations are as follows: Meters. Feet. Perry 206 677 Wilder 216 710 Wetunipka 172 565 Parker 170 558 Lowndesboro 121 396 Mount Carmel 192 629 Lovers Leap 169 556 Bargenier I 78 583 Count}' Line 173 56.S Ethridge 143 470 Fatama 165 540 Midway 171 562 Creagh '33 435 Pollard 121 397 The observations of the primary directions were made at night upon lights mounted over the respective stations. At Pollard .station it was nece.ssary to mount the theodo lite on a wooden .structure 199 No. 31. We.ogu.fkcL K/amieoTX,, 'y^e.tAjjmpha, FoTLcurd. Kilometers I H M MH -H- 10 20 30 40 Statute Miles 50 60 hH ^-1 v-i 1-1 1-^ 10 10 20 30 40 200 THE EASTERN OBLIQUE ARC. 46'53 meters (or 152 J^ feet) above the ground, in order to raise it above the high woods obstructing the hues of sight. Squaring the closing errors of the triangles we get the mean error V 28 -^' •08 I -08 and the mean error of an angle —y^ =±o""63, also the probable error of a direction, d=o"-30. Abslracls of horizontal directions at stations composing the fourth section of the triangulation ivest of the Atlanta base net, Alabama. /SSS-/Sgj. Jamison, Chilton County, Alabama. February I and March 5, 1889, and May 7 to 14, 1S90. 30*^™ repeating theodolite No. 16. F. W. Perkins and W. B. Fairfield, observers. Telescope 2"''i above the ground. Number of directions. Laurel Weogufka objects obser\'ed 3 Wilder 4 Perry Corrections Results from adjust- from adjust- ment of third section. ment of fourth section. Final seconds. O GO 59 "81 73 oS 57 -69 151 38 56-43 231 ID 29 '86 Mean correction -0-82 +0-05 -0-15 55 '61 29-91 Weogufka, Coosa Countj-, Alabama. May 28 to June i, and December 5, 18S8, to January 17, 1889. 30'^"' repeating theodolite No. i5. F. W. Perkins and W. B. Fairfield, observers. Kahatchee Wetumpka Wilder Jamison 00 59 -82 164 03 00-15 +0-67 00-82 200 00 45 -06 +0-14 45-20 260 22 41 -57 Mean correction +0-14 Wilder, Autauga Count}', Alabama. June 13 to July 28, 1890. 30"^"' repeating theodolite No. 16. F. W. Perkins, observer. Telescope 20"'-3 above the ground. Number of directions. objects observed 5 Wetumpka Montgomery, Capitol 6 Lowndesboro 7 Lovers Leap 8 Parker 9 Perry 10 Jamison II Weogufka .esults from station adjustment. Corrections from adjust- ment of fourth section. Final seconds. 00 00 •00 —0 ■32 // 59 •68 36 84 00 43 39 94 ■74 05 — •74 39 •00 99 41 48 -39 —0 -03 48 -36 145 24 54 -49 + -16 54 •65 176 38 20 -73 +0 -14 20 -87 226 24 43 -90 +0 •84 44 -74 267 32 52 ■91 —0 -05 52 -86 THE MAIN TRIANGULATION. 20 1 Abstracts 0/ horizontal directions at stations composing the fourth section of the triangulation west oj the /Itlanla Imse net, Alalmma, /,S&V-/,?^5— continued. Perry, Chilton County, Alabama. July 30 to Augu.st 6, 1890. 30"" repeatinj^ thcfKlolite No. r6. V. W. Perkin.s, observer. Telescope i""7 above the j^round. Corrections Results from station from adjust- Final adjustment. ment of seconds, fourth section. Number of directions. objects observed 12 Jamison 13 Wilder 14 Parker GO OfJ'fX) —0 '09 59 -gi 50 42 04 "96 "O -06 04-90 96 51 15-25 --0-I5 15-40 Wetumpka, Elmore County, Alabama. March 6 to May 23, 1892. 30'^"' repeatinj^ theodolite No. 16. F. W. Perkins, observer. Telescope i""8 above the ground. Off/ ff ff 00-30 19 Mount Carmel Montgomery, Capitol 20 Lownde.sboro 21 Wil 22 Weogut'ku II -21 35-29 47-19 Parlcer, Autauga County, Alabama. Augu.st 8 to 28, 1890. 30<^"' repeating theodolite No. 16. F, \V, Perkins, observer. 00 00 '00 +0-30 15 36 22-25 39 09 1 1 '09 ^0-I2 97 04 34-94 -^-0 -35 48 39 47-96 -0-77 15 Perry 16 Wilder 17 Lowndesboro 18 Lovers Leap DO 00 -00 —0-18 59 -Sz 102 37 25-30 -0-17 25-13 172 09 44-08 +0 -oS 44-16 203 32 39-76 -0-27 40-03 Loivndesboro, Lowndes County, Alabama. March 26 to April 25, 1892. 30^"^ repeating theodolite No. 16. F. W. Perkins, observer. Telescope 2o"'-3 above the ground. 23 Parker 24 Wilder 25 Wetumpka Montgomery, Capitol 26 Mount Carmel 27 Bargenier 28 County Line 29 Lovers Leap 00 00 'OO — 010 59 "90 49 oS 27-40 -^0-93 28-33 87 07 28-24 -0-13 28 -I I lor 49 4S -45 171 58 00 -86 —0 -20 00 -66 214 iS 04 -20 -0 24 03-96 241 53 56 -76 + 0-03 56 79 274 05 53 -00 —0 -29 52-71 Mount Carmel, Crenshaw County, Alabama. RLiy 26 to June i, 1892. No. 16. F. W. Perkins, observer. 30™' repeating theodolite 39 Bargenier 40 Lovers Leap 41 Lowndesboro Montgomery, Capitol 42 Wetumpka 00 00 -00 ^0 -39 28 34 48 -68 —0 -03 56 34 1 2 39 ^001 104 47 10-94 112 34 33 92 -0 -37 00-39 48 -65 12 -40 33 "55 202 THE EASTERN OBLIQUE ARC. Ahslracls of horizontal directions, at stations composing the fourth section of the triangulation xvest of the Atlanta base net. Alabama, iSSS-iSgj — continued. Lovers Leap, Lowndes County, Alabama. June 4 to 20, 1892. W. B. Fairfield, observer. Telescope 7'""5 above the ground. Objects observed. 30"™ direction theodolite No. 135. Circle used in XVII positions. Nnniber of directions. 32 Lowndesboro 33 Mount Carmel 34 Bargenier 35 County Line 36 Midway 37 Fatama 38 Ethridge 30 Parker 31 Wilder Results from station adjustment. Corrections from adjust- ment of fourth section. Final seconds. / // // // 00 00 -00 +0-04 00-04 49 52 45-80 +0-55 46 -35 75 30 10-39 — -04 10 -35 115 27 55 "55 +0 -II 55-66 142 57 02 -iS +0-I6 02-34 171 54 21 -51 —0-34 21-17 1S5 50 02 -19 —0 -09 02 -10 297 17 01 -14 -0-31 00 -S3 330 3S 43-38 -0 -08 4,^ -30 Probable error of a single observation of a direction {D. and A".), e^ = ± o'^-84. Ethridge, Dallas County, Alabama. June 6 to 11, 1892. 30"" repeating theodolite No. 16. Perkins, observer. F. W. 00 -24 26-61 21 16 Bargenier, Lowndes County, Alabama. March 18 to April 7, 1892. 30"^'" direction theodolite No. 135. W. B. Fairfield, observer. Circle used in X^VII positions. 53 Lovers Leap 54 County Line 55 Fatama 00 CO -00 40-24 51 57 27 -06 -0-45 153 22 20-95 +0 -21 43 44 45 46 County Line Lovers Leap Lowndesboro Montgomery, Capitol Mount Carmel 00 GO -00 -(-0-29 53 59 14-24 +0-07 98 41 16 -61 -fo-2I 132 30 40-19 179 47 04-09 -0-57 Probable error of a sii:.gle ob.servation of a direction {D. and R.), c'l :o"-72. 00 -29 14-31 16-82 03-52 County Line, Lowndes County, Alabama. May 10 to 16, 1S92. 30"" direction theodolite No. 135. W. B. Fairfield, observer. Circle used in XVII positions. 52 Bargenier 47 Midway 48 Fatama 49 Ethridge 50 Lovers Leap 51 Lowndesboro Probable error of a single observation of a direction {D. and A'. ) 00 00 -QC -0-44 59-56 138 31 49-80 -0-27 49-53 177 24 01 -35 -fo-19 01 -54 216 16 28 -96 +0-38 29-34 273 56 58-28 —0-42 57-86 306 17 06-94 +0-56 07 -50 and A'. ), t'. = ± 0" ■87. THE MAIN TRIANGULATION. 20' Abstrac/s of horizontal directions at stations composing; the fourth section of the trianf^ulation -ucest of the .Itlanta base net, /llabauia, j8S8-/S(js — continued. Fatania, Wilcox County, Alabama. October 2 to November 26, 1895. 30'"' direction theodolite No. 145. G. A. Fairfield, observer. Telescope I5"''8 above the ground. Circle used in XII positions. Corrections Results from station from adjust- Final adjustment. ment of sections, jourth section. Number of directions. Objects observed 59 Midway 60 Pollard 61 Creagh 56 Eth ridge 57 Ivovers Leap 58 County Line 00 00 '(X) —0 -04 59 96 67 24 iS-64 -^0-33 18 '97 96 02 10 '39 — '12 10-27 262 09 32-81 —0 "09 32 72 274 51 31 72 — '11 31 -61 301 52 12 -15 —0-03 12 -18 and R. ] , e, = ± "•5.8. Probable error of a single observation of a direction (D. and A". ), e^ Midway, Monroe County, Alabama. September 19 to October 20, 1S95. 30-"' repeating thecKlolite No. 16. F. W. Perkins, observer. Telescope 34""5 above the ground. 62 Pollard 63 Creagh Lookout Hill 64 Fatama 65 Lovers Leap 66 County Line 00 00 -GO -0-31 59 69 23 41 51 '42 — 0-2I 51 63 50 50 15 -83 82 29 45-86 —Oil 45 75 148 24 01 -So —0 -10 01 -90 165 29 48-23 +0-II 48-34 Creagh, Clarke County, Alabama. Augtist 9 to September 10, 1S95. 30 '" direction theodolite No. 1 ^5. G. A. Fairfield, observer. Telescope i2'"-4 above the ground. Circle used in XVI positions. White 70 Fatama 71 Midway 72 Pollard Red Hill 00 00-00 196 20 14-53 -0-30 14 23 221 30 12-95 ^0-41 13 36 270 04 55 -03 — o-ii 54-92 320 37 14-96 Probable error of a single observation of a direction (/). and R.), e,= zt.o""]6. Pollard, Monroe County, Alabama. Augu.st 29 to September 13, 1S95. 30""' repeating theodolite No. 16. F. W. Perkins, observer. Telescope 46"'-5 above the ground. 67 68 69 Red Hill White Creagh Fatama Midway * 00 00 00 55 52 09 -60 93 01 16-79 —0 -01 170 38 .48 -06 -fO-I2 200 44 46-47 — o-ii ♦The correction — o"-09 was applied for ecccniricity. 16 78 48 iS 46 36 204 THE EASTERN OBLIQUE ARC. I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX =+I = I = — o =+I 1 — 2 = — o =+o' = + r = — o = +r H-o = +o =+I = — o = — o = — o = +o :— O' = +o' = +o' ■—4' +o' =+3 -3' +5' : — I' +3' :-L2' — I' = +!■ +9' -6 = +5' Observation equatio7is. •84- (2)+ {3)-(io) + (ii) •92- (I)+ (2)+ (5)-(ll)-(2l)+(22) •60- (3)+ (4)- (9)+(io)-(i2)+(i3) •19- (8)+ (9)~(i3) + (i4)-(i5)^{i6) •24- (5)+ (6)--(20) + (2l)-(24)+(25) •19- (6)+ (8)-(i6)+(i7)-(23)+(24) •87- (7)^ (8)-(i6)+(i8)-(3o)-f-(3i) •72-(i7) + (i8)i(23)- (29)^(30)+ (32) •63-(i9)-t-(2o)-(25) + (26)-(4i)+(42) •2i-(26) + (27)-(39) + (4i)-(45)+(46) •o2-(27) + {29)-(32) + (34)-(44)4-(45) •65-{33)+ (34) -(39) + (4o)-(44)+ (46) o8-(34) + (35)"(43)+(44)-(5o)4-(52) •8o-(27)+(28)-(43) + (45)-(5i)+(52) 69"(35) + (38)-(49) + (5o)-(53)+(54) 97-(48) + (49)-(54) + (55)~(56) + (58) 2o-(37)+(38)-(53) + (55)-(56)- 61 -(47) 09-(35)- 33-(59) i4-(6o)- II-(62)- -(48)- -(36)- -(60)- -(61)- -(63)- -(5S)+(59)- -(47) +(50)- -(62) + (64)- -(67) + (6S)- -(67)-!-(69)- (64)4 -(65)4 (68)4 (70)-! (57) (66) (66) (69) (72) (71)+ (72) 3-2-90(1)4 4-10(2) I 0-82(3) -0-39(4) -I -72 (12) +3-74(13) -2-02(14) +0-47(15) 3i(i6)-o-78(i7) — i-32(2o)+2-99(2i) — i-67(22)-i-82(23)+4-52(24) — 2-70(25) 8 + 6-39(6)-7-54(7)-hri5(8)+o-78(i6)-4-23(i7)+3-45( 18) +1-08(30) 74(3i)+2-66(32) 0-0-22(5) + 7-76(6) -7-54(7) -2-58 (19) +3-90(20) -I -32(21) -3-74(31) 52(32) -1-78(33) -3-96 (4o)+5-38(4r) -1-42(42) 4-2-32(26) +3-55(27)-i-23(29)-o-55(32)+4-39(33)-3-84(34) -2-47(39) 86(4o)-i-39(4i) 3+2-80(27) -4-03(28) + 1-23(29) -1-0-55(32) -3-06(34) + 2-5 1 (35) +0-15(50) 55(5i) + i-4o(52) 3-o75(35)+8-49(37) -7-74(38) -2-6i(48)+3-94(49) -1-33(50) -6-81 (56) 35(57) -2-54(58) 5 + 2-65(35) -4-o5(36) + i-4o(37)4-4- 13(57) -5-44(58) + i-3r (59) +0-26(64) 84(65)+6-58(66) 6+0-87(59) -4-72(6o)+3-85(6i)+4-5i(62)-4-79(63)+o-28(64) +0-61(70) 86(7i) + i-25(72) I i THE MAIN TRIANGULATION. Normal equations. 205 '9 0=+0 '09 20 -0-33 21 +0-14 22 + 0-II 23 -4-3 24 + 3 '8 25 + 6-0 26 -1-4 27 + 2-3 2>S + 1-3 29 + 1-5 30 + 5-6 C, C5 C3 C4 Cs Cc C7 Ce C9 Ci . Cii C.I c, C.4 Cl^ C,', C.7 Cl!^ I o= + i-84 + 4 — 2 — 2 2 + 1 '92 +6 — 2 3 -I '60 +6 — 2 4 — o'i9 +6 — 2 -2 5 + 1 '24 +6 — 2 — 2 — 6 -2-19 +6 + 2 — 2 7 -o'Sy + 6 + 2 8 —072 +6 — 2 9 +0-63 +6 — 2 10 + I-2I +6 — 2 + 2 — 2 II — 0'02 +6 + 2 — 2 + 2 12 + 1-65 +6 — 2 13 +o-o8 +6 + 2 — 2 14 +o-8o + 6 ■5 + 1 -69 +6 — 2 + 2 16 -0-97 +6 + 2 -2 17 — 0'20 +6 18 — o'6i +6 Norvial a/ nations — completed. C22 C23 C24 C2^ C26 C27 C28 C25 - 3-28 + 2 '34 + 4 '25 - 5 '92 - 2 91 + 5 '25 - 0-31 - I '04 + 1-38 o'37 6-39 10-25 6-54 9 '26 - 2-66 276 776 3-80 5 '52 0-32 5-38 5 '52 + 0-6S - 0-93 + 6-95 - 8-07 - I '90 + 3-84 - 3 '55 + 2 +6 2 'So 5-i8 3 06 6-82 3-SS 2-36 2-36 + 0-58 + 2-65 — 12 26 + 10-82 — 007 — 007 — 0-58 +6 — 2 +6 +2 + 2 +6 - 2-65 - 5 "44 + 2-73 + 13-07 + 6-72 - 1-05 + 0-59 - 9 -82 + 9 21 — 6-19 -^92-50 + 3-54 - 9-10 + 151-64 +I35'i' +234 '99 — 1-46 +1 -46 -33 '61 + 3 '04 + 76-75 +19-87 +45 94 - 2-Ot> + 296-91 + 6-65 + 62-53 + 163 -90 + I -21 +86 -61 2o6 THE EASTERN OBLIQUE ARC. Resulting correlates. Ci = — 0780 C„ = +o'284 Coi = -|-o-242 C:,= — 0731 Ci2=— 0-249 C2, = — 0-237 C3=+0-055 Ci3=+0-I0S C23 = +0"02l8 C4 = +o-i93 Ci4=— 0-397 0^4=— 0-00S6 C5 = — 0-418 Ci5=— 0-390 C25=+o-or83 C6=+o-409 Ci6=+o-o58 €26=— 0-0760 0; = — 0-043 Ci7=-ho-i55 C27= -0-1070 Cg=+o-345 Ci8=+o-200 C28 = — 0-0184 C9=-o-345 C,9=+o-o67 C29 = -o-o237 C,o=- 0-326 C2o= +0-123 C3o=— 0-0944 Rcsiillini: CO! rections to observed directions. (0 = = +0-668 (19) = = +0-298 (37) = = -0-344 (55) = = +0-213 (2) +0-138 (20) +0 -116 (38) -0 -093 (56) —0 -088 (3) -0-817 (21) +0 -354 (39) +0 -387 (57) — 0-115 (4) +0 -046 (22) -0 -767 (40) —0 -029 (58) +0 -034 (5) —0-317 (23) —0 -104 (41) +0 -012 (59) —0 -036 (6) -0 -739 (24) -1-0 -926 (42) -0-371 (60) +0-327 (7) —0 -03 1 (25) -0-132 (43) +0 -289 (61) —0 -121 (S) +0-163 (26) -0-195 (44) +0 -073 (62) -0-312 (9) +0-138 (27) -0 -243 (45) +0-213 (63) +0-215 (10) +0-835 (28) +0 -034 (46) -0-575 (64) —0 -no (II) —0 -049 (29) -0 -286 (47) —0 -267 (65) +0 -095 (12) —0092 (30) — 0-311 (48) -rO-190 (66) +0-HI (13) —0 -056 (31) —0 -080 (49) +0 -375 (67) —0-005 (14) +0 -149 (32) +0 -039 (50) -0 -423 (68) +0-119 (15) -0-183 (33) ^0-550 (51) -0 -563 (69) —0 -114 (16) -0-173 (34) -0 -037 (52) -0 -438 (70) —0 -300 (17) +0 -083 (35) +0-113 (53) -ro -235 (71) +0-413 (IS) +0-272 (36) +0-163 (54) -0 -448 (72) -0-113 Probable error of an observed direction 0-674^ /^^ = =0 •34- Resulting angles and sides of the fourth section of the triangulation zcest of the Atlanta base net. No. Wilder Jamison Weogufka Wetunipka Wilder Weogufka Perry Jamison Wilder Parker Perry Wilder Observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. Log. dis- tances. Distances in meters. / // // // // 41 oS 09 -01 —0 -88 08-13 0-81 4-432 911 3 27 096 -38 78 29 5874 -0-S2 57-92 0-80 4-605 982 4 40 362 -91 60 21 56-51 -0-14 56-37 o-8i 4 -553 909 35 802 -14 51 35 13-02 — I -12 II -90 I -03 4-605 9S2 4 40 362 -91 92 27 07-09 -0-27 06-82 I -04 4 -71 1 520 4 51 466 -00 35 57 44 '91 -0-53 44-38 I -03 4 -480 740 5 30 251 -06 50 42 04 -96 + 0-04 05 -00 I -05 4 -553 909 35 802 -14 79 31 33 '43 +0-86 34-29 I -06 4 -657 953 4 45 493 93 49 46 23 '17 + 0-70 23-87 I -05 4 -548 055 3 35 322 -81 102 37 25 '30 +0-01 25-31 0-68 4 -657 953 4 45 493 '93 46 09 10 -29 -j-O -21 10-50 0-67 4 -526 629 6 33 622 -47 31 13 26 -24 -0 -03 26 -2 1 -67 4-3S3 230 I 24 167 •4r THE MAIN TRIANGULATION. 207 A'esn/tivff ang/es and sides of Ihr fourth section of the base net — continued. triani^ulatiou west of tlic Atlanta No. 13 14 15 16 stations. observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. Log. . -58 10 1 5« 5 1 79 76 30 5' -44 57 56 49-19 45 32 20 -09 103 3' tKl -32 34 53 "8 -33 4' 35 53 "63 52 46 41 -22 84 06 06 - 1 7 43 "7 12 -70 28 oS 24-66 52 56 49-91 9^ 54 47 ""3 Correc- tion. Spher- Spher- ical ical angles, excess. I^g. dis- tances. Distances in meters. ') -74 16 '37 r '20 — o -07 21-79 ' '9 — I -13 25 -42 I -19 +0-66 15-49 0-78 +0 -79 22 -27 o -79 +0 -62 24 -60 -79 +0-25 59-58 [-13 +0 -24 31-02 I -12 -f-o -oS 32 -78 r -13 -fo -29 28 -87 o -48 +0-42 15-92 0-47 —0-47 16-63 o '47 -o -20 57 -06 o -35 —0-51 18-82 0-36 —0-28 45-19 0-36 ^0-37 13-82 0-52 +0 -72 37 -94 o -52 +0-34 09-79 0-51 +o'i6 34 '32 0-63 1 0-07 44-33 0-63 +0-17 43-24 0-63 ■'^97 157 5 -594 430 « ■558 422 3 -594 429 9 -468 673 o ■507 C>02 9 -619 293 4 •694 251 8 -507 002 9 -694 251 8 ■397 629 6 •468 673 I •468 673 o -223 609 6 -402 402 o ■594 429 9 ■223 609 8 •6S3 316 4 ■6S3 316 4 -402 402 o ■507 003 o -0-51 10 ■62 -62 4-402 402 +0 -09 20 -00 ()-6i 4 -539 029 5 -0-47 3 ' -23 -62 4 '469 457 8 +0-36 58 ■17 0-63 4 -402 402 — -01 1 1 ■57 -63 4-479 341 +0 -36 52 ■15 63 4 '635 156 6 +0 -08 51 ■52 -63 4 '539 029 5 +0-27 49 •46 0-63 4-479 341 +0 -82 20 -91 -63 4-404 704 4 -0 -25 (X) -07 0-61 4 -635 '56 6 1 Q-IO oS •43 62 4 -404 704 3 -0 -28 53 '35 62 4-469 457 / rO-34 41 •56 0-47 4 -404 704 4 1 -62 06 ■79 0-46 4 -3"i 3 '3 3 + 0-35 13 •05 0-47 4 -338 386 5 +0-72 25 •38 -91 4-404 704 4 4 -50 5''' •41 -91 4 -633 149 4 - o-o8 46 ■95 0-92 4 -725 827 4 49 79' 1'^ 39 3'->3 -39 36 176-15 39 yi -38 29 422 -05 32 136-82 41 619 -17 49 459 -74 32 136-82 49 459 '74 24 982 -14 29 422 06 29 422 05 16 734-38 25 258-17 39 303 -38 16 734-39 48 229 -90 48 229 -90 25 258-17 32 136-83 25 258-17 34 596 -29 29 475 -27 25 25S17 30 153-73 43 167 -47 34 596 -29 3^* '53-73 25 392 -44 43 '67-47 25 392 43 29 475 -27 25 392 44 31 719-28 21 796-40 25 392 -44 42 968-43 53 189-68 2l8 THE EASTERN OBLIQUE ARC. Resulting angles and sides of the fifth and last sections of the triangulation west of the Atlanta base net — continued. No. 24 25 26 27 28 Stations. Observed angles. Correc- tion. spner- ical angles. »pner ical excess / rr // // // Fort Morgan 46 13 20 '60 +0-36 20 -96 0-96 St. Elmo 77 59 07 '81 +0-19 08 -00 0-95 Daphne 55 47 34 '33 —0 -42 33 -91 -96 Fort Morgan iS 04 55 -94 -0-35 55-59 0-51 vSt. Elmo 130 45 49-03 + 0-52 49-55 0-51 Spring Hill 3' "9 16-26 +0-13 16-39 0-51 Dauphin Island East Base 116 36 16 -20 -0-63 15 -57 -26 St. Elmo 16 02 14 -60 — -22 14-38 0-25 Fort Morgan 47 21 31 '27 — 0-46 30-81 0-25 Dauphin Island West Base .S7 37 43-50 + 0-39 43-89 0-55 St. Elmo 36 30 34-69 — 0-17 34-52 0-55 Fort Morgan 55 51 43 -92 ~o -68 43 -24 0-55 Dauphin Island We.st Base 78 40 21-17 - 0-91 20 -26 0-27 St. Elmo 20 28 20 -09 +0-05 20 -14 0-27 Dauphin Island East Base .So 51 20 -71 -0-31 20 -40 -26 Dauphin Island East Base 162 32 23-09 +0-94 24 -03 0-03 Fort Morgan S 30 12-65 —0-22 12-43 0-03 Dauphin ] sland West Base 8 57 22-33 + 1 -30 23-63 0-03 Dauphin Island East Base 44 34 26 -38 4-0-64 27 -02 -80 St. Elmo 94 ni 22-41 —0 -04 22-37 -80 Daphne 41 24 II -92 + 1 -09 13 -or 0-80 Dauphin Island East Base 72 01 49-82 -I -27 48 -55 0-41 Daphne 14 23 22 41 -I -51 20 -90 0-41 F'ort Morgan 93 34 51 -87 —0 -09 51-78 0-41 Log. dis- tances. Distances in meters. 4-501 323 ^ 31 719-28 4 -633 149 6 42 968 -45 4-560 278 o 36 331 -05 4-338 386 4 21 796-48 4-725 827 4 53 189-68 4-560 277 8 36 331 -03 4-560 277 9 36 331 -04 4-050 203 4 II 225-44 4 -475 527 2 29 890 -09 4-560 277 9 36 331 -04 4 '335 134 2 21 633-87 4-478 516 I 30 096-51 4 -475 527 2 29 890 -09 4 -027 831 9 10 661 -83 4-478 516 o 30 096-50 4-335 134 2 21 633-87 4 -027 831 9 10 661 -83 4 -050 203 5 1 1 225 -44 4-501 323 3 31 719-28 4 -654 020 6 45 083 -Si 4-475 527 4 29 890-10 4 -633 149 5 42 968 -44 4-050 203 3 II 225-44 4 -654 020 6 45 083 -81 Remarks on the accord of the Atlanta and Dauphin /s/and Imses. — The di.stance between the middle points of these bases, when measured through the middle line of the triangulation connecting them, is 677 kilometers or 421 statute miles.* The total number of geometrical conditions demanded by this triangulation in order to remove its inconsistencies is 142, to which number one more condition would hav^e to be added to bring out the length of the second ba.se as measttred. The simultaneous .solution of so large a number of equations being impracticable, the actual adjustment was made in parts. -When the Dauphin Island base was reached a very small difference f was found in the computed length, as derived from the Atlanta base, and the measured length, a matter of accident, but a very .satisfactory one, .since no further labor was needed to bring about a closer accord. * It is made up of the several parts as follows: In base net, 42 kilometers; first section, 98 kilometers; second section, 88 kilometers; third section, 80 kilometers; fourth section, 209 kilometers; and fifth section, 160 kilometers. fOne and a half units in the seventh place of decimals in the logarithm. THE MAIN TRIANGULATION. 219 12. THE FIRST SECTION OF THE TRIANGULATION WEST OF THE DAUPHIN ISLAND BASE NET, ALABAMA AND MISSISSIPPI, 1846-1855. Proceeding from the base net westward, the triangulation is contracted in dimen- sions and possesses an inferior degree of accuracy as compared with the triangulation north of the base. This change is primarily due t!g/ts and suffs of thi first section of the triangulation ivest of Dauphin Island base net stations. Observed angles, o / // Petit Bois 50 49 13 76 Point aux Pins 47 37 13 '21 Dauphin Island West Base Si 33 33 "66 Correc- tion. Grande Batture 54 50 Point aux Pins 88 51 Dauphin Island West Base 36 iS Grande Batture 105 37 Point aux Pins 41 14 Petit Bois • 33 08 Grande Batture 50 47 Dauphiii Island West Base 45 15 Petit Bois Horn Island East 1855 Grande Batture Petit Bois Baj'ou Ca.sotte Grande Batture Petit Bois Bayou Casotte Petit Bois Horn Island East 1855 Bayou Casotte Grande Batture Horn Island East 1855 East Pascagoula Bayou Casotte Horn Island East 1855 East Pascagoula Bayou Casotte Petit Bois East Pascagoula Petit Bois Horn Island East 1855 Belle Fontaine East Pascagoula Horn Island East 1S55 «3 55 53 71 57 26 04 28 01 '60 39 '39 19-97 27 '05 26-18 05 -s? 25 '45 13 "69 19 '63 50 -66 44-72 26-37 47 103 28 37 ■ ^o 09 -09 i3'5o 3' 36 52 47 26 47 -96 42 36 12-87 •"^9 56 59 '65 94 5S 25 -76 50 31 24-37 34 30 08 -99 57 107 14 20 155 3 56 52 10 42 19 58 20-18 39-62 5'"^ 73 28 -49 27-58 51 '69 37 13 38 38 104 07 58 -38 38 42 55 '8 95 12 56-0 46 04 07 -o Splier- Spher- ical ical angles, excess. Log. di.s- tances. Distances in meters. -0-17 13 '59 0-20 — o -05 13-16 o -19 -+^0-17 33-83 0-19 ^O -12 01 -48 O -15 -o'03 39 '36 0-15 —0-36 19-61 0-15 +0-36 27-41 0-13 +0-03 26-21 0-13 -|-o -89 06-76 0-12 +0-48 25-93 0-17 +0-53 14 '22 0-17 +0-73 20-36 0-17 -0-39 50-27 0-15 — o -69 44 -03 o -14 -0-23 26-14 0-15 + 1-23 39-03 o-io +0 -02 09 -I I O 'lO --I -34 12-16 o -10 -1-38 46-58 0-I4 + 1-10 13-97 0-13 +0-21 59-86 0-14 — o -j6 25 -60 o -09 +0 -71 25 -oS o "09 +0 -60 09 -59 o "09 +0 -47 20 -65 o -03 + 1 'oi 40 -63 o -04 -ho -09 58 -82 o -03 ~I TO 27 -39 O -02 — o -38 27 -20 o -02 05-47 O -02 + 1-57 53-26 0-I5 .... 08-51 0-I5 +0-30 58-68 0-15 + 1 -I 56-9 o-i -f O -4 56 -4 O -2 -fO "2 07 "2 O -2 4-193 605 2 15 617 27 4-172 673 o 14 S82 -40 4 -299 478 8 19 928 -69 4-193 605 2 15 617 -27 4 -281 040 2 19 100 -30 4 '053 513 2 II 311 '32 4 '299 478 8 19 928 -69 4-134 862 4 13 641 -5] 4 '053 5>3 J II 311 '32 4-172 673 o 14 882 -40 4 -134 862 2 13 641 -50 4-281 040 o 19 100-29 4-134 862 3 13 641 -51 4-121 942 o 13 241 -65 4 '196 033 9 15 704-85 4-134 862 3 13 641 -51 4-254 684 9 17 975 -66 3 -950 829 6 8 929 -55 4 -121 942 o 13 241 '65 4 -085 225 7 12 168-18 4-254 6S4 7 17 975 -65 4-196 033 9 15 704-85 4 -085 225 8 12 168-18 3 -950 S29 4 8 929 -55 4 -085 225 8 12 168 -18 4 -135 600 2 13 664 -70 3 -546 295 3 3 51S-00 4-254 684 8 17 975-65 4 -326 S12 5 21 223 -28 3-546 295 4 3 518-00 • 4 •121 942 o 13 241 -65 4-135 600 o 13 664-70 4 -326 812 5 21 223 -28 4-135 600 I 13 664-70 4-337 600 5 21 757 -07 4 -196 S38 o 15 733 96 THE xMAIN TRIANGULATION. 225 i^ 15 16 17 iS 19 Rcsultiiii::; aiii^lcs and f.id cs of Ihc fir si %C(iioii ( / Ike lriani:;ulation lucs I of Dai pliin Island bast net -continued Stations. observed angles. Correc- tion. Spher- ical an«le». Spher- ical excess. I,og. dis- tances. Distances in meters. / // // // // Horn Island West 42 18 49 fi -4 50 4 02 4-135 6 Ship Island 1S55 31 56 3«-5 -I '5 37 "o I 4-049 199 II 199-50 Deer Island i 103 49 5' -4 -0-2 51 -2 0-2 4-312 896 2 20 553 -99 Belle Fontaine 44 13 31 -9 +0-3 32-2 O'l 4-169 209 4 14 764-18 vShip Island 1S55 60 10 39 'o — •! 3!^ '9 "I 4-195 161 4 15 673 -34 Deer Island i 65 00 45 7 — 0'2 45 '5 02 4-214 177 3 16 374 -85 Horn Island West 1 Trio ATr-» 1 r^'^ 54 T r 48 36-8 -07 36-1 0-2 4 -169 209 5 14 764-19 ' 226 THE EASTERN OBUOUE ARC. 13. SECOND AND LAST SECTION OF THE TRI ANGULATION WEST OF THE DAUPHIN ISLAND BASE NET, MISSISSIPPI AND LOUISIANA, 1850-1S74. No. 34. Mississippi City Pitcher Point 2 Point Clear East Pearl River Rigolet Light LOUI SIANA Fort Wood nrrt ■^^¥' Island, Sou-th Point New Orleans, St. Patrick's Church Nine Mile Bayou envenue iProctor Point 1853 /McLrtello Tower JBcryou Pierre ux^oint Oyster Pavou. 1855 MISSISSIPPI Kilometers Statute Miles ^Caernarvon The second and last section of the triangulation stretches west from the Hne Deer Island I to vShip Island 1855 and reaches the astronomic station in the cit}' of New Orleans, Louisiana, a distance of 132 kilometers, or 82 statute miles. .It is of secondary and somewhat irregular character as to size and shape of its component parts, yet posse.s.ses sufficient accuracy to render it u.seful in the discu.ssion of the geodetic and astronomic measures of the southern portion of the oblique arc. When within 34 kilometers, or 21 .statute miles, of New Orleans the triangles are apparently left without a check, but here we can take advantage of a well-determined and independent length of the terminal side Martello Tower to Bienvenue. This is furnished by its direct connection, through a small but otherwise well conditioned and adjusted river triangulation, with the Magnolia liase line, .situated about 60 kilometers, or 3734^ statute miles, farther down the Mississippi River.* This base was measured by Assistant C. H. Boyd in January, 1872. Its length is, roughly, 3*6 kilometers, or 2^ .statute miles, t and the corresponding length of .side Martello Tower to Bienvenue is 6 233 "42 meters. The length for this same line, starting from the Dauphin Island base in the old unadjusted computation of 1880, is 6 233*02. The di.screpancy was removed by dispersing this difference in the adju,straent between this side and the .side Deer Island I to Ship Island 1855, at the .same time preserving the four intermediate and adjusted parts, as explained farther on. In this branch of the triangulation it was foinid sufhcient to give the resulting angles either from the .station adju.stment or from direct measure, as the case may be, to the nearest tenth of a second; further, the special tabulation of the.se results could be dispensed with, since they are given in the presentation of the triangles. * See sketch of tri.ingulation, plate No. 19, Coast and Oeodetic Survey Report for 1S79. tIservatioii equations. 0=+ 3-o-(i)+(2)-(4) + (6)- (8)+ (9) 0=+ o-4~(i) + (3)-(5) + (6)"(io)^(ii) o=- r7-(4) + (5)-(7) + (9)-(ii) + {i2) o=-4r9-o-68(i)+5-99(2)-5-3i(3)-2-o4(4)+3-68(5)-i-64(6)-5-39(7)+7-5o(8)-2-ii(9) Correlates and resullinase net. Obser\'e' ! angles. Correc- tion. Spher- ical angles. spher- ical exces.s. Log distances. Distances in meters. / / f // n // 42 21 51 -4 -07 507 0'2 4-169 209 14 764-17 70 44 54 7 +0-4 55-1 0-3 4-3'5 662 20 685 -3 66 53 14-8 -1 o-i 14-9 '2 4 '304 316 20 '5' 9 76 28 33-5 -0-5 33-0 0-3 4 '3 '5 662 20 685 -3 54 ID 30 '6 -0-3 30-3 -2 4-236 793 17 250-2 49 20 56-9 40 "5 57 "4 -2 4-207 942 16 141 -4 64 00 127 i DM 12 -8 O-I 4-207 942 16 141 -4 57 37 19 + 0-2 19-2 0"2 4-180 886 15 166 -5 5^ 22 29-1 -0-6 28-5 '2 4-184 451 15 291 -5 48 15 01 '4 -0-3 t)l T T 4-207 942 16 141 -4 24 39 28 -5 — O'l 28 "4 OT 3 '955 5i> 9 026 -32 107 05 3" '9 •(_) 30-9 0'2 4-315 551 20 680 -Q 94 54 55-4 [-0 '2 55-6 OM 4-180 886 '5 166 5 36 22 02 -3 1 c-i 02-4 OT 3 '955 511 9 026-32 48 43 01 -8 1-0-5 02-3 (} "1 4 -058 394 1 r 439 '2 46 39 54-0 to -5 54-5 -I 4 -184 451 15 291 -5 lOO 22 15-0 +0 -1 15 ■! 0-2 4-315 55' 20 680 -o 32 57 50 -5 +0 -3 50 8 'I 4 -058 394 11 439-2 79 59 I 2 -u -0-3 n 7 'I 3 -955 5'i 9 026 -32 43 50 36-5 — '2 36-3 e) X) 3 -802 717 6 349-17 56 10 12-5 -0-4 12 •[ •() 3-881 619 7 614 -11 31 43 28 ■() + 0-I 28-1 -1 3-881 619 7 614 -1 1 82 28 30 '3 'O 30-3 •! 4-157 014 14 355 -4 65 48 02 "O —0 'I 01 "9 •! 4-120 824 '3 207 '6 10 19 10 '9 I • I I r 'o 'O 3 '802 717 6 349 •'7 23 53 36-2 -0-8 35 '4 'O 4 '157 012 14 355 '3 ■45 47 14 -o -0 "4 '3-6 'U 4-299 466 19 928 • 1 58 23 12 -2 -07 " '5 -2 4-184 451 15 291 -5 63 5S 09-4 -0 7 087 '2 4-207 760 16 1347 57 38 4' ' "3 'O 40-3 •[ 4 • 1 80 939 15 168-4 40 28 33 '9 f- 1 -9 35 ••"! -2 4-:8o 939 '5 168-4 5'^ 33 52 T -\- 2 T. 54 ■' 0-3 4 -299 670 19 937 '5 80 57 29 '4 'I '5 30-9 o'3 4 -36 > '73 23 076-7 '9 04 14-9 'I 4-058 394 1 1 439 "2 22 09 46-5 -l-I -2 47 7 •] 4-120 822 •3 207-5 138 45 57-8 —0 "I 57 7 Q-I 4 -363 172 23 076 -6 No. '3 14 16 17 18 19 23 24 25 THE MAIN Tl ^lAXGl JLATIO X. 233 Ititifi ani;lcs and sides 0/ the si'coiid (/;/(/ last section of til e li i amenta! ion Ti'est of the Pauphin [xlan I tiase net — continued. Stations Observed angles. Correc- tion. Spher- ical angles. Spher- ical excess. I.^g. dis- tances. Di.stance in meters. / // // // // Point Clear 64 54 08 '4 ' '3 07-1 0-4 4-363 '73 23 076 7 Pitcher Point 2 57 06 43-' -0 -3 42-8 o'3 4-330 386 21 398 -6 Bayou Pierre 57 59 12 •! -9 I 1 2 0-4 4-334 601 21 607 3 Grand Island 1S52 84 46 367 1 ' -3 38-0 -2 4 -330 386 21 398 -6 Point Clear 57 34 03 -6 + I-I 047 f) -2 4 -25.S 550 18 '36-4 Bayou Pierre 37 39 17-1 [0-8 17-9 0-2 4-118 166 '3 1 27 Nine Mile Bayou 60 20 44-1 + 0-5 44-6 -2 4 -25.^ 550 18 '36 -4 Grand Island 1852 79 41 '9-3 -0 2 .'9 -I -2 4 3 ' 2 446 20 532 7 Bayou Pierre 39 57 57-2 -0 -3 56 '9 -2 4-127 275 '3 405 -3 Grand Island 1855 «3 22 26-6 + 0"2 26-8 0-2 4 -330 386 21 398 -6 Point Clear 59 3'^ 59 •« 4-0 -6 60-4 0-2 4-269 2S5 18 590 -2 Bayou Pierre 36 5S 32 "9 ho -5 33 '4 -2 4112 5>7 12 957-4 Nine Mile Bayou 52 39 39-2 I -o 38 -2 0-4 4 -330 3'^6 21 398-6 Point Clear 49 43 oS-i 0-3 4-312 446 20 5327 Bayou Pierre 77 37 14 '3 +0-5 14-8 0-4 4-419 772 26 288 -9 Grand Island 1S55 77 18 47 -2 +0-I 47-3 '2 4 -3 1 2 446 20 532 1 Bayou Pierre 40 3'"1 41 -4 Q-O 41 -4 0'2 4-137 CXJ7 13 709 Nine Mile Bayou 62 02 3 1 ■•'^ + ■ 1 3f9 0-2 4-269 286 18 59<^--3 Oyster Bayou 1855 94 "5 44-8 -4 44 "4 0-2 4-269 285 iS 590 -2 Grand Island 1S55 43 33 07-2 -o-S 06-4 01 4-108 621 12 841-7 Bayou Pierre 42 21 07-3 + 2-3 09-6 O'l 4 -09S 85 7 12 556-2 Oyster Ba^ou 1855 81 20 57 '2 ^2 -2 59 '4 00 4-137 tx)7 •3 709-0 Nine Mile Bayou 64 53 '9 9 Q-I 4-098 S57 12 556 -2 Grand Island 1855 33 45 40 • 1 r-o -8 40-9 CM 3 -886 843 / 706 25 Malheureux Point 56 26 46-2 • 0-9 47 ■' 4 -09« 857 12 556 -2 Grand Island 1855 77 47 23 '5 • 1 "5 25-0 4 - 1 68 0S3 '4 725 9 Oyster Bayou 1S55 45 45 4S-3 -0-4 47-9 4 -033 214 lO 794 -8 Malheureux Point 84 22 34 -6 + 1-9 36-5 4-137 W7 13 709 Grand Island 1855 44 01 43 '4 1-0-6 44 -o 3 '9'*^' 100 9 574 i-I Nine Mile Bayou 51 35 38 ■ 1 • I -4 39 "5 4 -033 214 IC. 794 -8 Malheureux Point 27 55 48-4 ;-0 -9 49 3 3 -886 843 7 706 -25 Oyster Bayou 1855 35 35 08 '9 : 2-5 II -4 3 -98" ICK) 9 574 -U Nine Mile Bayou 116 28 59 '3 4-168 083 14 725 -9 Rigolet Light 29 i;. 63 -2 3 '5 59 7 4 -033 214 10 794-8 Grand Island 1855 52 42 52 '3 ■ 11 -8 53 ■ ' 4 -245 179 '7 586 -5 Malheureux Point 98 ^'3 "7 '5 '3 07 -2 4 ■340 165 2 1 ■885 -9 P'ast Pearl River 55 47 55 -6 ■ I -I 567 4 -033 214 10 794 -8 Grand Island 1855 72 "4 21 5 -5 21 -o 4-094 055 12 418 -I ;Malhetu-eu\- Point 52 Grand Island 1855 Rigolet Light 144 57 41 '4 + 1 -2 42-6 4-340 165 21 .S85 -9 19 21 29-2 ~i '3 27-9 4-101 599 12 635 -7 15 40 45-1 +4-4 49-5 4 012 961 10 303 -0 vShell Point 69 28 43-5 - -8 427 4-245 179 17 586-5 28 > Rigolet Light Malheureux Point 79 39 ii -4 -0-5 32-9 4 -266 540 is 473-1 30 51 43 ■ + + I-0 44 '4 3-9S3 750 9 632 -74 Fort Wood 29 40 097 — 2 -I 07 -6 3-983 750 9 632 74 29 \ Rigolet Light 36 II 18 -6 +0-6 19-2 4 -060 338 II 490-5 vShell Point 114 oS 33 7 -0-5 33 '2 4 -249 405 17 758-4 f Proctor Point 1S53 49 28 307 — I -Q 297 4 -060 338 II 490-5 30 1 Fort Wood 61 1 8 27-9 -0-3 27-6 4-122 559 13 260-5 I Shell Point 69 13 02-5 -i-O -2 02 7 4-150 236 14 133-0 Martello Tower 31 > Fort Wood Proctor Point 1853 69 35 34-5 -Oj 34-2 4 -150 236 14 133 -0 45 3? 02 -8 4-031 758 10 75S-7 64 53 22-6 4-0-4 23-0 4-135 271 13 654-3 Batter}' Bienvenue 32 l-'ort Wood [ Martello Tower 95 '9 50 '3 -I -6 487 4-135 271 13 654-3 27 02 oS-o 3 -794 728 6 233-44 57 3« 05 -o -I 7 03-3 4-063 829 II 583-2 Ducros 45 40 33 'o 'O 33-0 ■ 3 '794 727 6 233 -42 33 \ Bienvenne 82 GO 03-1 +0-I 03-2 ■ I 3 -935 932 8 628 -44 Martello Tower 52 19 23 '9 -Q 23-9 • 3 -838 615 6 896 -27 Caernarvon 44 49 59 7 + 1-3 61 -o • I 3 -935 932 8 62S-44 34 Ducros 95 j8 19-8 + 1-4 21 -2 • I 4 -085 848 12 1S5-6 Martello Tower 39 51 367 + 1-3 38-0 CO 3-894 517 7 843 -63 Saint Patrick's Church (center) 27 1 1 44-4 " -2 44-2 ■! 3-894 517 7 843 -63 35 ■ Ducros 97 16 17-0 ~o -3 167 -I 4 -231 066 17 024 -2 - Caernarvon 55 31 59 '6 —0 '2 59-4 • I 4 -150 739 14 149-4 THK MAIN TRIAXGULATIOX. 235 re 14. SOME STATISTICS oi" THK TKIAXOULATION. In the following tal)le will bo found some statistics relatin<^ to the trianj.(nlati(;n. In the third column is given the number of triangles contained in this discussion, including those few triangles of which but two angles were measured. In the next column is given the mean error of an angle derived from the relation m — ^/ , whe A — closing error of a triangle and u the number of triangles; in tlie last ccjhunn is given the more precise measure of accurac>', namel\', the probable error of an observed direction derived from the adjustment of the triangulation, given by the formula: iVpvv] ^^ = o"674-/ where z' = the correction required by the figure adjustment,/ its weight, usually unity, and c — number of conditions that entered into the adjustment. Locality or name. Kpping base net. Northea,stern boutiilary section. New England section, connecting three base lines. Fire Island base net. Section connecting the Fire Islanil and Kent Island bases. Kent Island ba.se net. Allegheny .section, to Humpback — Spear.* First section .south of the tran.sconti- nental triangulation. Second, or North Carolina section. Third, or South Carolina section. Atlanta base net. Fir-st .section west of Atlanta ba.se net. Second section west of Atlanta base net. Third .section west of Atlanta ba.se net. Fourth .section west of Atlanta base net. I'ifth and last section west of Atlanta base net. Dauphin Island base net.f First section west of Dauphin Island ba.se net. Second section we.st of Dauphin Island base net. Total number of trianj^les Weighted mean State. Number of triangles. Mean error of an angle. // Number of con- ditions satisfied. Probable error of an observed direction. /I Maine. 46 z!rO-63 35 =047 Maine. iS 074 13 "•51 Me., N. H., Ma.ss., R. I., 5?, <' Si 57 26 Conn. Connecticut, New York. '7 49 16 034 N. Y., N. J., Penn., Del., 33 -se 35 047 Md. Maryland. 12 -96 13 041 INIaryland and \'ir<;inia. 28 0-94 22 " 35 \'ir^inia and North Carolina. Yirginia and North Carolina. N. C, S. C, Ga. Georgia. Georgia and Alabama. Alabama. .■\labama. Alabama. .■\labama . .•\labania. .Vlabania and Mississippi. .Mabama and Mississippi. 2S o -SS 24 0-41 II I j" 13 72 35 078 41 62 33 I 'OO 29 -65 25 0-97 23 079 16 078 18 67 13 077 14 '36 28 63 30 034 2S 0-6S 28 '35 5 051 5 026 19 078 18 53 4S5 461 * Kstiniated for two quailrilalerals beyond line Mount Marshall to Bull fof little weight on account of the small extent. :oS2 Run. o 78 ±05 1 C. RKvSULTiNG GKOGRAPHIC POvSlTIONS OF THK PKIN-CIPAL STATlONvS OF THE TRIANGULATION BKTWF:KN CALAIS, MAIXIv AND NEW ORLEANS, LOULSIANA, BASED UPON THE CLARKE SPHEROID OF 1866 AND THE DATA OF THE TRANSCONTINENTAL TRIANGULA- TION. The geographic positions in the following list are those used in this investigation of the figure and size of the earth. They conform to those published in vSpecial Publica- tion No. 4, "The Transcontinental Triangulation." These positions, as well as those in Special Publication No. 4, are not intended to Ijc used for geographic purposes, and do not conform to the principal lists heretofore published for that purpose, namely, for Massachusetts, in the Report for 1894, Appendix No. 10; Rhode Island, in the Report for 1885, Appendix No. 8; and Connecticut, in the Report for 1888, Appendix No. 8. On March 13, 1901, the Superintendent adopted a uniform standard for the whole United States, to which all positions intended for geographic purposes are to be reduced and which is to be known as the United States Standard Datum. The New England positions referred to al:)ove are leased upon the United States Standard Datum. The corrections required to reduce the po.sitions here published to the United States Standard vary at different parts of the arc, and in general fall between the limits Jcp = + i"'9 to -f 2"-i, AX = — o"'5 to ~ o"-8, Aa= — i" to -f- 2". stations. Latitude and longitude. ,\/.iniuth. Hack a/.imtith To stations. I,og. dis- tance. Distance in meters. Ne7v ByuH$7vick. Chamcook 45 07 28-347 345 52 03 *6o 165 55 08-78 Prince Regents Redoubt 4-37' 372 8 23 5>6-5I <=>7 05 02 797 63 13 17-88 242 57 00 -70 Cooper 4 529 929 I 33 878-88 Graiul Manan ■14 44 51 '626 93 12 51 'lo 273 01 oS -6^ Trescott Kock 4 342 006 7 21 978 94 66 49 54 '371 143 23 18-98 323 15 43 ■07 I'rince Kegeiits Redoubt 4 376 239 23 781 -49 St. David 45 15 00 -878 319 44 57 74 '39 5' 2' ',« Chamcook 4 262 200 iS 289-42 ^ Maine. 67 14 03 -514 46 50 37 '49 226 42 28 -44 Rye 4 315 000 5 20 653 -82 Againeiiticiis 4.^ 13 22 '638 2 36 55 '9-' 1S2 35 23-16 Thoni psou 4-S32 776 9 68 041-97 70 41 .«'S3i 70 12 55 '05 -'49 ■f' !0 -39 Uiikonoonuc 4-890 346 8 77 686-72 Bnrkf 44 35 54 '036 235 13 08 -22 ,55 19 08 -45 Kpping Kast Base 4 •13'^ 343 6 '3 75" -30 67 5S ?i -319 337 01 27 -04 '57 05 01 -62 Pigeon 4 -23S 8476 17 35>'96 Calai.s Ob.servatory 45 1 1 03 "778 206 54 46-96 26 5ft 47 '9' St. David 3-9>4 328 3 8 209-72 67 i6 ,53 '919 293 06 27-23 1 13 14 51 '42 Chamcook 4-227 Si6 4 16 897-26 Cooper 44 59 ' > '570 35' 53 09 -93 171 S'' io-9,>/ Howard 4-603 402 I 40 123-80 67 28 03 -393 75 09 42 '97 -',54 42 27-80 Hnmptiack 4-720 S93 2 52 5*8-79 Eppiiifj Ka.st Base 44 4(1 07 •84.( -'77 06 5S'49 97 25 23 3 1 Howard 4 543 "7 5 34 923-48 f'7 49 ,S''^'595 10 52 25 -53 100 50 00-47 Pigeon 4-3*4 324 6 24 228 -59 Epping West Hase 44 41 29 '93^ 286 51 55 ' ' 7 H)6 5^ 21 42 Kpping Kast Base 3 940 3M 3 S -15 -^^ 67 5*^ ^TMl 1? 55 06 -50 '95 53 32 -'9 Burke 4 -032 670 S 10 7S1 -30 238 THE EASTERN OBLIQUE ARC. stations. Afaine — contimied. Howa rd Humpback Mount Blue Mount Desert Mount Harris Mount Independence Mount Pleasant Pigeon prince Regents Re- doubt Ragged Mountain Rye Sabattus Trescott Rock Nt'iu Htunpi/iii t'. Gunstock Monaduock Mount Washington Unkonoonuc Maasach usetfs. Blue Hill Copecut Great Meadow Latitude and longitude. 44 37 44 '677 67 23 46 '486 44 51 48770 68 06 3.8 -896 44 43 39 '450 70 20 3.1 '175 44 21 oj'joS 68 13 38729 44 39 52 '920 69 oS 55 730 43 45 31 774 70 ig 15 '306 Azimuth. Back azimuth. To statiotis. 65 14 114 5S 9 16 75 IS 341 59 26 19 78 30 115 46 52 IS 94 jS 2fi 55 72 46 oS -So 25 70 19-46 57 '53 1 1 '.59 26 -58 45 '89 16-62 27 '54 42-84 48-38 34 '95 244 39 294 28 1S9 II 254 35 162 10 205 59 257 52 295 o- 231 39 273 48 206 40 252 03 1 1 -.85 1479 24 -63 06 -04 16-31 17 '53 02 -56 31 '34 24-14 19-48 27 '15 08 -40 Mount Desert Humpback Mount Desert Mount Harris Sabattus Mount Pleasant Ragged Mountain. Mount Harris Sabattus Mount Blue Agamenticus Gunstock 43 31 02306 300 32 51-33 121 00 45-86 Agamenticus i9 43 23-05 219 13 02-94 Monaduock 71 12-299 42 51 39-141 336 14 22-31 72 06 31 -641 32 59 09-94 44 16 12-057 3 39 08-74 71 18 14-620 236 02 04-01 42 5"^ 57 ■■^45 24 06 11 -in 71 35 20-266 72 29 09-91 42 12 41 '933 71 ofi 53 '495 41 43 15-238 7" 03 37 '477 41 52 43 ''27 71 13 03-129 41 55 36-706 70 35 28-985 1 16 02 50 -31 155 43 43 '52 133 IS 12-60 175 17 04-04 123 44 54 '33 192 54 33 '99 59 44 28 -05 126 18 32-57 156 23 22-41 Wachusett 212 37 15-13 Mount Tom 1S3 36 23-95 Gunstock 56 42 29-47 Mount Blue 203 54 01 '87 Wachusett 252 07 55-50 Monaduock 295 31 36-62 Wachusett 335 24 28 -28 Unkonoonuc 313 02 35-32 Beaconpole 355 '4 52-96 Blue Hill 303 35 33 '64 Beaconpole 12 58 41 '54 Blue Hill 239 25 42 -09 Copecut 305 57 29-89 Blue Hill Log. rlis- Distance in tance. meters. 4-863 229 o 4-794 490 4 4-761 268 o 4-929 927 o 4-S34 04S 9 4-938 61S 6 4 a77 280 4 4 -909 249 6 4 '973 438 4 4 "977 267 I 4-824 135 I 4-94S 470 6 4 -647 630 o 4 737 944 " 4 '365 932 I 4-579 231 4 4 -655 000 3 4729 513 I 72 984-22 62 300-34 57 712-25 85 099-50 68 241-56 86 819-76 75 3S4'2i 81 142-72 94 067 -24 94 900-20 66 701 -43 88 811 -78 44 01 34 -698 306 12 05 '15 126 32 58 -37 Mount Independence 4 -699 925 8 50 no -16 70 49 22-903 38 06 09-79 217 43 27 '36 Gunstock 4-855 408 I 71 6x1 -66 44 27 16-964 159 01 42-47 338 52 24-67 Humpback 4 '687 346 9 48 679 '59 67 53 25-321 243 33 55 '23 63 54 42-96 Ho-ward 4 '641 374 5 43 789 '96 44 55 09 '523 23 21 55 '30 203 17 47 74 Trescott Rock 4-289 384 2 19 470 -82 67 00 41 "OIO loi 53 09 -22 281 33 48 -83 Cooper 4-565 481 2 36 768-95 44 12 43 '434 84 26 23 '93 263 47 37 '44 Sabattus 4-872 442 9 74 549 '19 69 09 06 -369 180 16 01 -14 16 08 -59 Mount Harris 4 '701 544 4 50 297-27 45 07 22 -680 269 30 22 -00 89 44 53 "6^ Chamcook 4 -429 504 7 26 884 -67 67 25 32 -890 12 16 1 3 -96 192 14 27 '44 Cooper t 4-190 727 15 514 '11 44 08 35 -85S 24 31 20-64 204 21 16-42 Mount Independence 4 '671 377 7 46 922-13 70 04 44-734 77 57 07-94 257 26 04-67 Mount Pleasant 4-785 231 " 60 986 - 1 2 44 45 30-33S 57 50 42 -10 237 38 34 -60 Ho-svard 4-430 277 26 932-52 67 06 32 -099 131 56 03 ■3S 311 40 52 '33 Cooper 4 -580 099 7 38 027 -67 44 38 21 -352 244 50 15 71 64 56 52-13 Eppiug West Base .4 '137 32S 2 13 ■,.9-18 68 05 41 -166 295 35 27 -52 115 40 29 --14 Burke 4-021 662 3 10 511 '44 4 '805 515' 8 63 902 -20 4 '975 2S7 4 94 468-59 4-654 798 1 45 164-59 4-913 165 6 81 877 '7° 4-923 24S I S3 ^00-79 4 -962 91S 5 91 816-03 4-77S S30 2 60 093-87 4-648 835 I 44 548-71 4 -S49 420 1 70 700 - 1 1 4 '973 491 2 94 078 -68 44 425-27 54 694 '54 23 223 74 37 951 '7' 45 IS5'63 53 643 -00 • THK MAIN TRIANGULATION. 239 stations. I * Thouii>son 42 36 39 '930 351 21 40-40 171 27 17-43 Manomet 4 -885 726 S 76 864 -6s 70 43 50-053 120 44 30-14 300 09 30 -63 Cnkonoonuc 4 ■910 955 81 461 (jT) Wachusett 42 29 18755 24 17 32-42 204 04 5S-y6 Bald Hill 4 797 545 62 740 07 7' 53 14 '835 66 36 43 -04 246 05 55 -97 Mount Tom 4 '835 503 ' 68 470-4! h'/iud,' /shiiid. Beaconpole 4' 59 40 '450 146 50 03 -48 326 32 26-18 Wachusett 4-817 279 5 65656-77 7' 27 02-094 228 55 17-53 49 08 47 -86 Blue Hill 4 -565 581 4 36 777 "43 Connecticut. Bald Hill ( Fairfied Co. ) 41 12 47-787 354 16 31 -28 174 18 35-50 West Hills 4-648 135 6 44 477 01 73 2S 42 -425 53 21 43 '93 233 14 00-54 Round Hill 4 SI' 236 3 20 475 'SS Bald Hill (Tolland Co.) 4" 58 23-S5I 47 57 30 '50 227 47 12-01 Box Hill 4 459 356 2 28 797-59 72 1 1 55 '844 82 45 17-34 262 04 10-02 Ivy 4 933 714 3 85 844 -VS Box Hill 41 47 .57 748 47 47 iS-30 227 27 37-22 Sandford 4-745 910 55 707 03 72 27 22-205 97 22 57 -97 276 52 12-72 Ivy 4 -S&S 420 3 64 33' 0.) Ivy 41 52 16-434 20 ,54 57 -85 200 44 26 -86 Wooster 4 79' 5'3 4 61 S74-74 73 13 28-707 533 >4 05-75 1.53 25 02 -99 Sandford 4-707 138 I 50 949 29 Mount Tom 42 14 2S-749 308 30 oS-92 128 48 15 -19 Bald Hill 4-678 iSo 7 47 662 -93 72 38 55 -874 16 12 13 -22 196 00 09 -S3 Sandford 4 955 070 ' 90 171 -67 Round Hill 41 06 1 1 -097 355 06 36-16 175 07 57-15 Harrow 4-531 267 4 33 9^53 -45 73 40 26 -520 93 36 48-78 273 31 24 -.58 Buttermilk 4-061 771 2 II 528-46 Sandford 41 27 40 743 29 14 57-16 208 .56 10-16 West Hills 4-914 716 82 170-50 72 57 00-074 -4 53 48-60 254 32 26-29 Wooster 4-669 171 46 6S4-31 Tashua 41 15 35778 16 39 34 -41 196 32 40-09 West Hills 4712 561 3 51 5S9-,5o 73 15 02-0S3 74 53 51 '31 254 44 .50-,s6 Bald Hill 4-296 541 3 19 794 35 Wooster 41 21 01 -906 296 42 15-07 116 51 40 -62 Tashua 4-348 S36 2 22 327-30 73 29 1S-SS3 354 55 05 '52 174 57 33 '8- West Hills 4-776 212 59 732-68 New York. 1 Buttermilk 41 06 34 '358 337 18 08 -70 157 24 52 -90 Harrow 4 '573 62S 3 37 465-22 73 48 39-626 50 48 43 -39 230 33 55 '67 Weasel 4 -61 1 542 6 40 882-98 Fire Island East Ba.se 40 40 01 '370 72 59 54-96 252 53 42-31 Fire Island West Base 4-147 953 5 14 058-97 73 03 20 -690 185 32 47 '29 5 .W 40 57 Kuland 4-296 291 I 19 7S2-95 Fire Island West Base 40 37 47708 ■39 03 50 "98 318 55 34 -92 West Hills 4-454 543 27 198 -38 73 12 52-757 212 43 36-41 32 50 43-00 Kulaud 4 452 173 4 28 325 -23 Harrow 40 47 53 '430 46 46 40-35 226 23 41 -32 Beacon Hill 4 -856 466 7 68 622 -52 73 38 22 '949 78 54 41 -49 258 26 35 -67 Sprinsjtt'ield 4-791 0099 61 80304 RuUind 40 50 39 -695 84 27 43 -20 264 12 iS-67 West Hills 4 522 397 > 33 296-39 73 01 59-070 158 27 26-10 33S 18 51 -86 'I'ashua 4-695 S47 6 49 641 -81 West Hills 40 4S 52-117 S4 14 38-01 264 06 14 -93 Ham>w 4 -25'^ 590 2 iS 158-03 73 25 33-130 146 57 23-22 326 47 37 -59 Round Hill 4-5S2 434 I 38-232-62 Ne-cV Jersey. Beacon Hill 40 22 24-457 54 04 37 -07 233 55 44 '04 Disboro 4 -381 0S6 I 24 048-59 74 13 42 "595 89 II 18-23 268 52 02 -70 Mount Rose 4 -624 192 8 42 091 -55 Burden 39 31 46-807 92 19 43 -45 272 06 19-93 Buck 4 ^ro 550 7 30 16S -29 75 22 53-468 125 42 11-79 305 29 34 -66 Meetinshou.se Hill 4-541 913 34 826-82 240 THE EASTERN OBLIQUE ARC. stations. Aeiu Jersey — cont'd. Disboro I^ippincott Moinit Holly Mount Rose Sprinfffield Stony Hill Weasel Pennsylvania. Bethel Willowgrove Yard Delaware. Meetinghouse Hill Mat yland. Finlay * Hill* Kent Island North Base * Kent Island South Base * I,instid'' Marriott * Latitude and longitude. 40 14 46 '206 74 27 26-539 o9 43 iS '439 75 I s 50 -435 40 00 06 '997 74 47 20-003 40 22 o] -305 74 43 26 '437 39 47 51 ■9S2 74 ,S9 36725 40 41 20 -056 74 21 25-.S7.S 40 07 10 -408 74 3-1 ,S3'452 40 52 34-725 74 II 12-916 39 50 44 '1 07 75 29 25-964 40 15 01 -301 74 .5.S 14 '585 40 o.S 29 -.S20 75 06 22 -930 39 5S 22 -673 75 23 14 -426 ,^9 32 24-651 7.=; 43 ,S.5 ■7'"^4 39 42 44 '148 75 42 40 7^ .\zimuth. Back azimuth. To stations. lyOg.dis- Distance in tance. meters. 76 31 29 "oSo 38 53 52 767 76 52 50 -328 38 58 24 -429 76 20 27 -924 .^^ .S3 ,Si 787 76 21 58 -789 39 o.S 19 '591 76 29 09 '376 38 52 25-417 76 .36 35724 36 59 09-68 120 42 48 -60 15 13 27-12 88 20 56 '06 37 44 05-93 86 35 25-41 336 08 37-91 52 17 5571 73 01 33 '85 1 20 07 49-05 342 40 01 -47 41 07 50-79 53 3'' 10 '91 116 48 03-07 280 28 06-31 3 37 06 -77 312 12 38-26 345 02 04 -97 337 47 32 '53 52 41 13 '57 299 41 39 '27 .»45 47 3376 347 17 37 '09 31 59 46-98 67 06 19-17 104 07 31 -29 5 21 32 -IS 62 20 38-41 39 24 25-852 354 34 26-29 20 18 03 -46 94 38 26-59 1.59 55 24-59 64 4 1 GO 'oX 135 37 .59 '69 ^2 ,53 40-15 141 47 26.42 24 16 04-75 90 M 4 7 '.58 96 37 35 '04 166 46 12 -26 Maryland Heights* 39 20 25-561 358 43 10-54 77 43 00 -445 34 00 56 -52 216 54 21 -32 Stony Hill 300 32 27 -66 Mount Rose 195 10 52-12 Burden 265 05 42-10 Meetinghouse Hill 217 36 13-36 Pine Hill 266 J 2 20-93 Yard 156 14 09-32 Ston>' Hill 232 10 17-61 Newtown 252 49 15-97 I.ippincott 299 52 39 '94 Vard 162 45 02 -54 Beacon Hill 220 53 32 -66 Mount Rose 233 30 10-43 Mount Holly 296 34 55 '1 2 Newtown 100 49 34 -50 Harrow 183 35 29-31 Beacon Hill 132 19 24-93 I.ippincott 165 06 15 -62 Burden '57 52 38-39 Mount Holly 232 34 02 -22 Willowgrove ■19 53 55 03 Mount Holly 165 51 54 -70 Pine Hill 167 20 26-24 Lippincott 211 55 48-61 Bethel 246 55 43-41 Turkey Point 283 57 06-28 Principio 185 20 44 -31 Buck 242 og 24 -37 Principio 174 35 54 '68 Linstid 200 12 20-76 Webb 274 25 17 09 Peach Grove 339 51 27 -46 Stabler 244 30 52-03 Marriott 3'5 32 31 "31 T^instid 262 44 29-64 Marriott 321 43 41 -57 Taylor 204 1 1 23 -97 Marriott 270 27 37 -96 Webb 276 27 23-21 Hill • 346 43 44-42 Webb 178 43 40-38 Bull Run 213 42 33 '59 Mount Marshall 4 '245 277 5 4-420 656 6 4-344 465 5 4 '532 5.S4 6 4 '456 957 7 4 709 403 7 4 '477 625 9 4-325 374 2 4-458 328 4 4 '589 931 4 4 '564 49S I 4 '675 473 3 4 '342 240 8 4 '509 657 7 4-671 752 6 4 747 79S 8 4 '310 393 6 4-559 914 6 4 '473 9S4 7 4-298 6S5 8 4-494 280 7 4 '595 230 7 4-456 145 5 4 -221 948 9 4-414 063 I 4-382 796 4-283 056 5 4 '454 159 6 4 "550 3'6 3 4-574 261 9 4 -4S2 609 8 4-420 998 3 4 •411 765 7 4 '253 398 2 4 '328 444 o 4-143 529 ' 4 '417 956 2 4 '214 204 4 '373 7'9 9 4 '392 324 7 4707 753 2 4-87S 122 3 17 590 '47 26 342-48 22 103-73 34 0S4 -32 28 63S -99 51 21576 30 034 -88 21 I53'ii 28 729-52 38 898 -37 36 6S5 -81 47 366-72 21 990-79 32 333 '87 46 962 -65 55 949 '84 20 435 '89 36 300-67 29 784-12 19 892 -33 31 209 06 39 375 '92 28 585-48 16 670 'SI 25 945 '56 24 143 '27 19 189-18 28 455 -06 35 507 '19 37 519 '92 30 381 '54 26 363 -21 25 808 -67 17 922-48 21 303-16 13 916-47 26 179-19 16 375-86 23 643 94 24 678 -84 51 021 -49 75 530 49 * Stations in common with and fixed by the transcontinental triangulation. THE MAIN TRIAXGULATION. 241 stations. Ma>y/a lid— continued. Osboriies Ruin * Principio Pooles Island* Soper* Stabler* Sugar Loaf* Swan Point* Taylor* Turkey Point* Webb* / 'ijginiu. Buffalo Bull Run* Cahas Clark* Flat Top Fork* Humpback* lyOnK Mountain Mount Marshall* Peach (irove* Rogers Smith IMountain Latitude- and longituile A ziniuth. Hack aziniutli. To stations. Log. dis- tances. J.)istancc in meters. ' " 39 27 52 796 c 555 3S 26-43 t n 175 39 06-70 I'oolcs Island 4 i"! 337 20 014 14 76 16 53'430 73 07 42-15 252 58 25-92 I-'inlay 4-340 289 4 21 892-20 39 35 34 '552 I 34 34 -59 181 34 22 -88 Turkey Point 4 -203 937 15 993 -26 76 00 17 '006 59 II 31-99 239 00 57 -So Osbornes Ruin 4 -443 000 9 27 733-26 39 17 o5-6«i 41 27 16-64 221 18 51 -52 I.instid 4 462 716 4 29 021 -27 76 IS 49-954 121 II 55-79 301 02 00 -38 l-'inlay 4 -419 418 8 26 267-50 39 05 09 703 268 49 18-14 88 39 42-70 Webb 4 -376 775 7 23 810-90 76 57 01-286 343 50 29-3*^ 163 53 07 -29 Hill 4 337 076 I 21 730 -82 39 07 15-569 43 31 30-39 223 22 16-17 Peach Grove 4 -48.8 456 8 30 793-34 76 59 07 •050 114 01 10-52 293 45 41 -37 Sugar I.oaf 4 ,586 513 6 58 593-45 39 '5 42-412 32 29 22-28 212 17 39-05 Bull Run 4-699 551 7 50 067 01 77 23 37 -423 107 30 00-24 2S7 17 43-59 Maryland Heights 4 -465 432 7 29 203 -35 39 oS 2,S -277 15 47 5S-81 ■95 45 40-90 Kent Island North Base 4 -286 689 I '9 350-36 76 1 6 49 -060 71 56 57 -47 251 49 10-42 Linstid 4-272 151 I '8 7'3-33 38 59 46-243 42 39 34 -28 222 34 07 -97 Marriott 4 -266 49S 5 iS 471-34 76 27 56-483 170 19 43 -07 350 >8 57-15 Linstid 4 018 I9S 2 10 427 93 39 26 56-156 50 19 42-97 230 10 02 -89 Pooles Island 4 -454 483 8 28 476-32 76 00 35 -405 94 21 30-60 274 u 09-07 Osbornes Ruin 4 -370 101 8 23 447 -78 39 05 24 '413 39 54 36-51 219 46 51-13 Hill 4-443 72' ' 27 779-29 76 40 30-733 97 22 49-52 277 n 05-40 Stabler 4-432 017 4 27 040-67 36 47 44 -069 2 28 57 42 -54 49 14 21 -99 Cahas 4 -735 69.8 6 .54 412-49 So 2S 39-565 253 08 13-16 73 41 04 -05 Smith Mountain 4-928 312 3 84 7S3-69 38 52 51 -450 22 30 41 -85 202 ig 28 -81 Clark 4 -^35 447 1 6s 461 -61 77 42 I3'I45 75 02 38-38 254 43 51-26 Mount Marshall .( -652 400 4 44 915 -93 37 06 59 -770 225 4S 35 -67 46 04 19-60 Flat Top 4 -72: (.63 5 53 415 04 So 00 57-165 285 47 27-89 106 03 44-13 Smith Mountain 4 -619 220 5 41 61218 38 iS 38 -975 63 09 16-78 242 36 05 -03 Humpback 4 -945 8 19 I 8S 271 -22 78 00 12 -025 117 25 51 -89 297 10 2S -99 Fork 4 -608 326 9 40 581 -39 37 27 04 -683 249 54 24-62 70 oS 44 -49 Tobacct) Row- 4 -567 0S3 6 36 904 -86 79 34 5S -92S 291 56 16-53 112 14 21 -Sg Long Mountain 4 -676 543 2 47 483-55 38 28 42-681 35 52 1 1 '94 215 34 15-71 Humpback 4 -S60 307 4 72 494 -8S 7S 24 57 -999 66 26 43 -47 245 53 1S-19 Klliott Knob 4 -933 S7S S 85877-38 37 56 53-769 88 32 08 -02 267 57 00 -So Bald Knob 4-922 915 2 83 736-58 7S 53 57 -777 123 40 43-29 303 25 22-28 Klliott Knob 4 -640 543 9 43 706-28 37 17 25-480 192 40 49-96 12 47 40 77 Humpback 4 -874 224 9 74 S55-71 79 05 10-772 163 09 09 -28 343 05 20 "So Tobacco Row 4-502 SS6 7 3" S33-67 38 46 31 -688 341 17 18 -02 161 24 45 -90 Clark 4-735 SS3 3 54 435 -64 78 12 10-S13 29 26 44 -10 209 iS 45 -18 I'ork 4 '5" 8 10 3 57 827 73 38 55 10-601 84 11 2 1 -So 263 55 30-60 Bull Run 4 -616 253 41 32S-S2 77 '3 47 -327 159 34 44 '75 339 28 32 -6g Sugar Loaf 4 "607 957 7 40 546-91 36 39 33 -968 332 46 i2 -04 153 00 20 -50 l\Hir(.' 4-883 517 2 76 474 -60 Si 32 42-378 40 46 10-34 220 24 47-93 Roan Ilis;h lUulT 4-918 217 4 S3 S35-67 37 00 49-354 I -8 ■3 04 -37 358 12 27-17 l-'lat Top 4 -686 522 9 48 5S7-51 79 33 57 -454 234 04 31-61 54 21 54-41 Long Mountain 4 r.-o ,VU 3 52 521 IC * Stations in common with and fixed bv the transcontinental triangiilntion. 4192 — No. 7 — 02 16 24'- THE EASTERN OBLIQUE ARC. stations. / 'irgi/na — coiitiiiuei Spear* Tobacco Row * Nortli Carolina. Benii King Mount Mitchell Ivatitude and loiia:itude. Back azinintli. To stations. Log. dis- Distance in tance. meters. Roan High Bluff Young Soiitli Carolina. Hogback Mauldin Pinnacle Wofford Georgia. Academy Atlanta Middle Base Atlanta Northeast Base Atlanta Southwest Base Blood Currahee Grassy 3- 33 40751 90 43 50-62 7845 47 '192 164 25 09-04 37 33 53 '594 124 40 32 -20 79 'I 26 704 211 01 07-74 35 33 52 -827 220 IS 10-43 ■^i 39 38 '032 257 56 53 '55 35 12 25 '649 141 33 39 '31 Si i,S 46 '057 225 34 50 '93 35 45 51 '44 196 27 56-26 S2 15 55 '02 291 50 44 -49 36 23 51 '403 1 58 33 32-10 So 16 59 '75^ 196 34 48 '69 36 02 45 '446 216 DO 54 -42 81 09 2474* 243 19 33 '69 36 05 33 '179 273 01 48-50 82 oS 44 '634 323 02 32-54 35 44 12-276 126 52 52-65 80 3S 51 -665 204 00 42 -26 35 10 10 '003 232 22 49-92 82 17 26782 305 44 12-69 34 49 16 '196 157 26 59-56 82 38 05 '506 236 56 13 '57 34 56 27 '015 203 23 41 -77 82 24 40-474 267 18 15-89 35 01 58 -585 249 39 13-79 82 44 30 '447 2S8 36 31 -38 34 57 30 -072 200 18 39-13 Si 56 07-174 243 53 46-98 33 57 30 '366 82 42 39-78 83 59 28 -860 153 06 53-34 33 54 19 '447 232 08 09-06 .84 16 38-136 312 22 32-71 33 55 55 '564 126 iS 04-86 ■84 14 09-791 191 36 22-37 33 52 49 '53° 232 06 51 -76 84 18 5675S 297 51 14-29 34 44 20 -949 246 34 02-45 S3 5fi 13 -609 294 15 38-14 33 59 33 '442 223 31 55-32 85 00 50 '358 272 34 29-97 34 31 42-855 188 10 26-00 83 22 33 706 244 14 58-60 34 29 oS-2So 232 01 27 -85 84 19 53 '408 267 37 13-27 270 28 12 -oS Tobacco Ro%v 344 20 08 -66 Humpback 304 16 1615 Bald Knob 31 II 50-01 Humpback 40 35 51-27 Poore 78 32 iS -85 Young 321 21 34-31 Benn 45 58 00-43 Young 16 32 oS-Si Roan High Bluff 112 II 53-77 Benn 338 26 34 -89 Buffalo 16 44 24 -74 Cahas 36 25 06 19 Buffalo 63 50 32-14 Moore 93 36 44 -46 Poore 143 19 34-95 Benn 306 34 58 00 Poore 24 1 3 34 -64 Moore 52 44 43-12 Benn 125 56 27 Si Wofford 337 23 19-17 Pinnacle 57 03 53 -95 Paris 23 27 50 -87 Hogback 87 34 37-37 Wofford 69 54 47 -43 Hogback 108 47 53 -70 Paris 20 28 10 -iS Benn 64 15 15-08 King 262 34 27-87 Atlanta Norlhea.st Base 333 01 II -19 Saw nee 52 09 31 -84 Atlanta Northeast Base 132 26 55 60 Stone Mountain 306 10 41 -94 Sweat Mountain ■I 38 54 -02 Sawnee ■ 52 09 31 -84 Atlanta Northeast Base 117 56 .54-30 Stone Mountain 66 55 53 '35 Rabun 114 34 46-12 Currahee 43 44 36-86 Pine Log 92 49 04 -34 Kenesaw 8 13 02-19 Ralnin 64 40 16-60 Mauldin 52 14 54 33 Blood S7 57 55-37 Skitt 4-577 326 2 4 -649 283 4 4 -849 042 s 4-696 339 5 4 -846 167 o 4-971 70S 4 4 -705 136 6 4 -925 530 7 4-579 630 9 4-771 325 I 4 -676 356 4 4 -920 554 3 5-013 257 o 4-943 028 7 4-950 523 6 4 -S64 269 I 4-758 644 5 4-904 942 5 4-858 124 o 4 -602 019 6 4 -405 5S6 3 4-3S6 965 5 4-441 543 7 4-638 655 I 4-641 697 5 4 '503 290 4 4-S55 901 2 4 -800 210 3 4 -358 1 17 9 4 -538 n\ 2 3-6S3 590 2 4 -215 64S 3 4 -401 456 3 4 -536 834 8 3-970 276 I 4 -249 470 6 4 -802 267 7 4-752 074 5 4-701 967 7 4-604 I S3 7 4-689 285 I 4 -876 702 I 4-661 044 2 4 -748 161 8 37 785-59 44 594-72 70 638-72 49 698 -07 70 172-51 93 693 -2S 50 715-02 84 242-39 37 986 -64 59 064 -30 47 463-13 83 282-60 103 099 -60 87 705-88 89 232-61 73 159-22 57 364-67 80 341 -98 72 131 -33' 39 996-28 25 444 -05 24 376-17 27 640-36 43 516 -62 43 822 -54 31 863-27 71 763-10 63 126-29 22 809-61 34 540-94 4 826-03 16 430-41 25 203-24 34 421 -90 9 33S -48 17 761-13 63 426-06 56 503 -39 50 346-31 40 196-08 48 897 -33 75 283-90 45 818-85 55 996-62 ^Stations in common with and fixed by the transcontinental triangulatiou. THE MAIN TRIANGULATION. 243 I^atitiide and Stations. lyHiuune and longitude. Azimuth. Hack a/iniutl To stations. UOg. (US- 1 tance. Distance in meters. Georgia — cotitinued. ' " ' / // Gulf Point M 37 29■V,2^ 270 21 36-61 90 34 1 1 -56 Johns 4 529 537 9 33 849-3'* 85 28 02 •S24 356 37 55 '63 176 39 21 -02 Indian 4 -820 337 I 66 120-65 Johns 34 37 20-912 308 08 41 '.SS 128 24 21 -18 Pine Log 4-732 129 53 967-09 85 05 54 -122 27 40 24-62 207 33 .57-13 Lavender 4 ".576 176 5 37685-70 Kenesaw 33 58 32 -066 172 06 >3'42 352 04 16-70 Pine Log 4 -587 666 4 3« 696-03 84 34 46-078 228 28 51 '33 48 32 59-86 Sweat Mountain 4-182 214 9 15 213-00 Ua vender 34 19 17-249 269 51 11 -27 90 13 13-30 Pine Log 4 '777 750 « 59 944 70 85 17 18-719 325 09 29'15 145 18 44-08 Games 4 '647 387 9 44 400 -50 Pine Log 34 19 ifi-ooo 236 55 16.98 57 05 38 -84 Grassy 4 -525 240 9 33 515 '13 84 3S 14 '012 28 2 00 14-29 102 16 20 'I I Sawnee 4-651 920 I 44 866 -28 Kabun 34 57 53 '468 ■ 261 24 26-47 81 43 38-«« Pinnacle 4-711 876 7 51 50S-24 S3 17 59 '673 284 30 08-34 104 52 57-92 Mauldin 4 -798 278 I 62 846 07 Sawnee 34 14 09-823 150 29 47-95 330 24 01 -28 Grassy 4-502 751 8 31 S23-7S 84 09 39-192 233 23 17-41 53 38 oS-81 Skitt 4 -700 538 9 50 180-95 Skitt 34 30 18-269 142 52 18-89 322 44 .59 •4S nlood 4-5'3 146 5 32 594 -66 83 43 20-214 265 12 55 '59 85 24 41 -92 Currahee 4 -503 Soi 31 900 76 Stone Mountain 33 4S 19771 149 23 30 '53 329 20 30-22 Atlanta Northeast Kase 4-212 738 2 16 320-68 84 08 46 -239 220 08 00-33 40 13 11 06 Academy 4 346 400 3 22 202-42 Sweat Mountain 34 03 ,S9-I38 149 27 55 '40 329 21 48-91 Pine Log 4-516 0.84 I 32 815 -S9 Alabama 84 27 21 -883 235 15 57-16 .55 25 53 -73 Sawnee 4-519 739 5 33 093 '26 Alpine 33 24 40-292 141 33 51 -36 321 23 17-60 Cahaba 4 -676 196 3 47 445 '64 86 12 27-492 257 27 29-92 77 40 41 -45 Cheehahaw 4 '579 .566 6 37 981 02 Aurora 34 08 45 -=,03 236 06 3' -43 ,56 21 03 -04 Brandon 4 -677 999 5 47 643-04 86 II 01 -III 280 12 46-25 100 38 16-17 Indian 4 -852 202 7 71 154-56 Pargeuier 31 .S9 14-452 135 47 09 -65 315 40 32-78 Lovers Leap 4 '44^ 35S 9 2S 077 -53 86 36 51 -350 iSo 29 12-15 29 17-59 Lowudesboro 4 '497 668 4 3' 453 '46 Brandon 34 23 05 -005 224 31 17 -22 44 41 00-81 Gulf Point 4 '573 iSS 9 37 427-34 85 45 13-034 322 21 46-56 142 32 50 -86 Indian 4 -695 S37 9 49 640-70 Cahaba 33 44 45-ilS 215 23 39-56 35 .35 07 -67 Aurora 4 736 436 7 54 505 05 86 31 33 '365 293 18 11 -30 113 42 00-72 Cheehahaw 4 -S60 S04 4 72 577 '90 Cat Island 30 18 54-274 316 16 59 '55 136 19 12-69 Dauphin Island East Base 4-009 213 8 10 214-42 88 12 38-851 22 45 27-88 202 44 20 -97 Dauphin Island West Base 3 962 492 9 9 172-61 Cedar Point 30 20 42-488 8 07 4 ' -93 iSS 07 13 '05 Dauphin Island East Base 4 034 45S 5 10 S25 -76 88 07 17-561 45 50 55 '"T 225 47 06-07 Dauphin Island West Base 4-22S 357 16 91 8 -51 Cheeliahaw 33 29 05-692 154 46 13-71 .^,■^4 33 42-57 .Aurora 4-909 145 I Si 123-30 85 48 31 -422 210 19 49 '60 30 32 36 -45 Indian 4 -845 763 S 70 107-39 Cold Creek 30 57 25 -027 17S 54 28-95 35S 54 16-99 Coon 4 -507 002 9 32 136 82 88 05 20-666 25S 07 44 '44 78 17 03-22 Dean 4 -468 673 29 422 05 Coon 31 14 4S-35S 229 07 3S-35 49 16 37-46 White 4-55* 422 2 36 176-14 88 05 43'8l' 275 44 45 'SlS 95 5S 16 -99 Red Hill 4 619 293 4 41 619-17 County Hue 31 57 50-224 175 3S 53 -09 .3,55 3"* i>'^'09 Lovers Leap 4 '357 27S 3 22 765-56 86 48 12-714 261 41 54 -81 81 47 55-63 Bargenier 4-257 I20 iS 076-73 Creagh 31 36 11 -130 232 4S 02-18 53 02 09-41 Fatuma 4 '-25 276 4 55 122-24 87 41 03-677 306 32 42-87 126 30 37-61 PoUanl 4-415 967 1 26 059-56 Daphne 30 36 05 -762 114 19 01 -13 294 11 37-90 Spring Hill 4 -4CM 704 4 15 392 '44 87 54 16 -946 190 49 52-66 10 51 41 -67 Minette 4-4?J 341 30 '55 r? 244 THE EASTERN OBLIQUE ARC. stations. Latitude and longitude. Azimuth. Back azimuth To stations. Log. dis- tance. Distance in meters. Alabama — continued. ' " ' " Dauphin Island Kast jO 14 54 '447 165 06 03 -75 345 03 37-99 St. Elmo 4-475 527 2 29 890 -09 Base .?S 08 14 -813 2S1 42 19-32 lOI 45 46-33 Fort Morgan" 4-050 203 4 11 225 '44 Dauphin Island West ^^0 14 19-561 264 1 1 23 -52 .84 14 43 '35 Dauphin Island East Base 4-027 831 9 10 661 -S3 Base SS 14 51-558 273 oS 47-15 93 15 33 '90 Fort Morgan 4 -335 134 2 21 633-87 Dean 31 00 40-292 131 43 27-82 3" 33 54 72 Coon 4 '594 429 9 39 303-38 87 47 15-226 20S 52 32-11 28 56 27 -58 Red Hill 4-397 629 5 24 982-13 Ethridge 32 04 43-931 245 52 52-05 66 00 24 -52 Lovers Leap 4-387 868 6 24 426 -92 87 03 29-565 297 50 iS -42 117 58 24-57 County Line 4 '434 991 6 27 226 -49 Fatama 31 33 31 '091 219 09 31 -86 39 15 12-97 Ethridge 4-427 241 S 26 744 '95 87 14 13-528 258 52 11-33 79 05 56 -77 County Line 4-620 873 3 41 770 -85 Fort Morgan 30 13 40-307 149 07 17-14 329 01 23-61 St. Elmo 4 560 27S 36 331 '05 88 01 23-757 195 20 38-09 15 24 14-17 Daphne 4 '633 149 6 42 96S -45 Fort Morgan, A.st Az. 30 13 40-301 93 15 36-00 273 oS 49-27 Dauphin Island West Base 4 '335 120 3 21 633 '17 Station 1847 .SS 01 23 -784 143 59 50-69 323 56 52 -27 Cedar Point 4 -206 143 7 16 074 73 Gunter 34 34 04 -490 297 43 27-43 117 57 40 -83 Brandon 4-638 579 6 43 509 '05 86 10 20 -627 1 16 10-17 ;Si 15 47 '32 Aurora 4-670 3S9 7 46 S15 -51 Horn 33 17 50-262 135 37 34 '97 315 33 u '83 Alpine 4 '247 564 17 6S3 -33 86 04 28-886 229 51 58-12 50 CO 45-06 Cheehahaw 4 '509 625 5 32 331 '47 Indian 34 01 47 -60S 201 16 29 -13 21 21 05 -89 Lavender 4 '540 524 3 34 715 '57 85 25 31 -412 276 05 34 -QI 96 19 22-45 Carnes 4 -582 375 3 38 227 -45 Jamison 32 55 54 -510 218 27 36 -25 38 36 44 -49 Kahatchee 4 -621 350 2 41 S16-74 86 3S 21 -461 259 07 53-40 79 17 10 -87 Weogufka 4 '432 9" 3 27 096 -38 Kahatchee 33 13 36-299 214 45 04-57 34 50 06 -42 Alpine 4-396 361 24 909-27 86 21 37 -002 253 32 15 -48 73 41 39 '37 Horn 4 '443 056 7 27 736 -82 Laurel 33 23 49'oi4 1S7 32 11 -55 7 34 01 -55 Cahaba 4 '591 482 6 39 037 -55 86 34 52-286 267 17 39-53 87 29 59 89 Alpine 4 '541 410 I 34 7S6 -45 Lovers Leap 32 10 07 -200 177 27 23-26 357 26 43 -40 Parker 4-641 191 I 43 771 -46 86 49 iS-648 240 10 22 -47 60 17 06-35 Lowndesboro 4-358 925 22 852 -04 Lowndesboro 32 16 15-5S1 146 II 13-53 326 03 47 '53 Parker 4 '591 oSi 3 39 001 -50 86 36 41 -140 195 19 41 -96 15 23 28-61 Wilder 4-619 619 3 41 650-41 Midway 31 43 03 -463 137 05 ,59 '66 316 59 59'ii Fatama 4-421 772 3 26 410-24 87 02 49-417 220 06 02 -24 40 13 4476 County Line 4 '553 155 5 35 740 -08 Minette 30 52 07 -453 112 50 33-81 292 43 03-26 Cold Creek 4-402 402 25 258-17 87 50 43 -649 199 17 30-87 19 19 18 03 Dean 4 -223 609 6 16 734 -38 Mount Carniel 32 01 14-072 81 43 25-91 261 34 58-84 Bargenier 4-404 518 7 25 381 -58 86 20 54 -584 138 17 37 '94 318 09 14 30 Lowndesboro 4 -570 946 7 37 234 -60 Parker 32 33 46-821 153 54 03-18 333 50 22-76 Perry 4 -383 230 1 24 167-41 86 50 33-110 256 31 28-49 76 42 44 -26 Wilder 4 -526 629 6 33 622 -47 Perry 32 45 31 -igo 236 59 07 -26 57 09 25 -61 Jamison 4 '548 055 3 35 322 81 86 57 21 -552 287 41 12 -26 107 56 10-47 Wilder 4 '657 953 4 45 493 -93 Point .\ux Pins 30 22 01 -836 300 03 57 -(,5 120 07 05-54 Cat Island 4-061 419 I II 5i9'ii 88 18 51 -990 335 41 32-18 155 43 33-50 Dauphin Island West Base 4-193 605 2 15 617-27 Pollard 31 27 46-614 204 17 09-00 24 24 18 -I I Fatama 4717 767 52 211 -60 87 27 50-666 234 23 07-18 54 36 13 '60 Midway 4-686 81S 9 48 620 -44 Red Hill 31 12 30-412 153 26 19-69 333 21 45-01 White 4 '493 964 7 31 186-36 87 ,39 39 '49° 213 32 II -So 33 38 20-43 Pollard 4 -529 843 I 33 872-18 1 THE MAIN TKIANGULATIOX. 245 stations. Latitude and longitude. A/.imiitli. I! ick azimuth. To stations. Log. dis- tance. Distance in meters A Id ba ma — continued / ■»„ / '/ 1 Kowe 34 32 19 -964 264 12 11 -28 84 24 09 -49 Ounter 4 "51 1 '49 9 32 445 -'6 Hfi 31 26 '930 354 26 07 -69 174 27 27-52 Summit 4 '572 1 15 2 37 3.34 9 > St. Khno 30 30 32 -402 198 15 34-06 18 17 44-69 S))ring Hill 4 -338 386 5 21 796-49 1 88 13 03 '031 251 02 15-61 71 1 1 48 -oS Daphne 4 'SO' 323 3 31 719-28 1 Spring Hill 30 41 44 '.SOS 190 40 37-82 10 42 23-26 Cold Creek 4 '469 457 8 29 475 27 1 88 oS 46 '420 236 14 48 -44 56 24 02 'ss Minette 4 539 029 5 34 5'/i29 Summit 34 12 13 -980 215 20 58-80 35 31 34-'<> (Sunter 4-695 149 2 49 562-05 86 29 05 -522 282 56 19-01 103 06 28 -15 Aurora 4-454 925 I 28 505-27 Weognfka 32 58 39 '195 178 54 29-13 358 34 18 -02 Kahatchee 4-44' 562 5 27 64 '-55 86 21 16 '659 216 17 59-26 36 27 10-16 Horn 4 -643 871 6 44 042 -46 Wetumpka 32 32 01 '458 111 27 30-94 291 17 49-29 Wilder 4 -480 740 5 30 251 06 86 II 38 -672 163 02 42-85 342 57 30'I2 Weo.gufka 4-711 520 4 51 466 00 White 31 27 35 -857 216 23 55 '91 36 27 48 - 1 1 Creagh 4-295 003 9 '9 724-40 87 48 27 -684 269 19 44 97 89 30 30 -60 Pollard 4-514 017 4 32 660-09 Wilder 32 37 59 '434 157 42 34 "34 337 37 51 -32 Jamison 4-553 909 35 -50214 86 29 38 754 198 50 42 -47 18 55 14 -50 Weognfka 4 -605 9S2 4 40 362-91 Wilson 34 2.S OS "140 243 29 09-45 63 39 07 '40 Rowe 4 -478 573 3 30 100-47 86 49 03-198 307 42 52-90 127 54 oS-oi Summit 4 -588 392 3 38 760-76 Wornock 33 .S9 46-272 220 24 31 -96 40 31 41 -84 Summit 4-481 194 5 30 282 -69 Mississippi. 86 4> 52 -2SS 330 oS 31 -89 150 14 16 -83 Cahaba 4-505 134 1 31 998 -r? Rellefontaine 30 20 3" '277 269 35 12-7 89 40 10 -3 Kast Pascagoula 4-196 838 '5 733 -96 88 42 34781 5 21 57-4 1 85 21 40-0 Horn Island West 3-994 61S 8 9 S76-86 Bayou Casotte 30 19 42 '575 273 40 46-49 93 43 34 '91 C'.rande Batture 3 -950 829 4 S 929 -.55 88 30 47 -883 8 39 12-09 1 88 38 37 -5.S Horn Island East 1855 4 085 225 7 12 I6S-1S Cat Island 1852 30 14 14-036 133 46 36 'o 3'3 43 09-2 Pitcher Point 2 4-180 939 15 I6^ -37 1 89 04 04 -370 192 09 47 -4 12 10 51 '7 Mississippi City 4 "207 760 16 134 -67 Cat Island 1S55 30 14 13 -S64 192 1 1 08 -4 12 12 12-8 Mississippi Cit}- 4 207 942 16 14 ■ 43 89 04 04 '655 268 39 41 -4 8S 45 06-2 Ship Island 1S55 4-236 793 17 250-15 Cat Island Light 30 13 48-673 170 07 52 -7 350 07 15-7 Pitcher Point 2 4 -05S 394 11 439 ''6 89 09 40 -973 265 02 .48 -3 85 05 37-6 Catlsland 1S55 3-955 511 9 026 32 1 Deer Island i 30 21 41 '040 281 11 25-1 101 14 ^2 -9 Hellefontaine 4 -049 199 11 199-51 88 49 26-110 320 00 30 -s 140 03 40 -9 Horn Island West 4-195 161 4 15 673 -.U East Pearl River East Pascagoula Grande Batture Horn Island East 1855 Horn Island West Mississippi City Petit Bois 30 10 .56-193 290 33 5' '7 110 36 52 -8 Grand Island 1-^55 4 012 962 10 302 -96 89 31 27-272 346 21 48-4 166 22 43 -3 Malheureux Point 4-004 0.55 12 418-09 30 20 33 ■.593 296 30 53-20 116 31 52 -72 Bayou Ca.sollc 3 -546 295 3 3 518-00 88 32 45-725 3.54 27 13-86 174 27 38 -76 Horn Island East 1855 4-135 600 2 '3 (64-70 30 W 23 -846 244 29 ,S8 -.38 64 33 1 1 -.54 Point .\ux Pins 4 053 5 '3 2 II 3>'-32 88 23 14-320 299 19 59 -87 119 25 13-89 Dauphin Island W est Base 4-281 040 2 19 100 -30 30 13 i: -goi 223 08 47-17 43 12 09 -83 I'.raiule Batture 4 196 03>> 9 15 704 "85 88 31 .56 -341 278 35 37 -43 98 39 43 '74 Petit Bois 4121 942 '3 241 -65 30 15 10-92S 239 09 04 -5 59 ■4 19-1 East Pascagoula 4-287 S27 7 19 401 -16 88 43 09 '3,i" 281 27 54 -9 101 33 .V -8 Horn Island East 1S55 4 --^3 971 9 IS 364-10 30 22 46-232 275 39 51 '7 95 46 11-4 Deer Island 1 4 304 316 20 151 -90 89 01 57-046 318 01 42 '5 138 06 03-6 Ship Island 1855 4 'o'S 662 10 685-31 30 12 07 -389 170 oS 09 -S8 3.50 07 25-80 Grande Batture 4-1.^4 Sfi 2 •3 (v»I -50 88 23 46-844 254 05 30-25 74 09 59 -67 Dauphin Islaiul \\ est Base 4-172 673 14 8S2 •411 h6 THE EASTERN OBUOUE ARC. stations. Latitude and longitude. Azimuth. Back azimuth To stations. Log. dis- tance. Distance in meters. A fississip/ii— continued. Pitcher Point 2 30 19 54 '661 249 45 00-5 69 49 32 -0 Mississippi City 4-184 451 15 2gi '53 89 10 54-368 313 45 13-3 133 48 39-9 Cat Island 1855 4-1S0 886 15 166-52 Point Clear 30 15 47-120 -'49 17 24-4 69 23 46 "I Pitcher Point 2 4 '334 601 21 607 -32 89 23 30 -982 314 II 31-4 1.14 16 19-7 Bayou Pierre 4-3.^0 386 21 398 -63 Ship Island 1S55 30 14 26 -509 204 59 '8-5 25 01 16 -3 Deer Island i 4-169 209 5 14 764-19 88 53 19-661 265 09 57-4 85 15 04 -s Horn Island West 4-214 177 3 16 374-85 South Point 30 11 13-376 128 55 i6-i 308 53 24-6 Cat Island Light 3-881 619 7 614-11 89 05 59 -440 208 54 27-7 28 55 25-5 Cat Island 1S55 3-802 717 6 349-17 Loiiiiiatia. Battery Bienvenue 29 59 02-847 219 38 iS-8 39 40 36-8 Fort Wood 4 063 829 11 583-21 S9 52 51 -433 314 58 07 -5 134 59 29-6 Martello Tower 3-794 728 6 233 -44 Bayou Pierre 30 07 42 -355 192 15 30-9 12 17 03-3 Pitcher Point 2 4 -.563 173 23 076 -66 89 13 57-793 232 44 06-7 52 J9 05-1 Cat Island 1852 4 -299 670 19 937 -47 Caernarvon 29 51 49-307 177 55 53 -0 357 55 47-7 Ducros 3-S94 517 7 843 -63 89 55 15-512 222 45 53-9 42 48 27-7 Martello Tower 4 -085 S47 12 185-60 Ducros 29 56 03-.SS0 216 56 53-5 36 58 10-7 Battery Bienvenue 3 -838 614 I 6 S96-27 89 55 26 -070 262 37 26-5 82 40 05-7 Martello Tower 3 -935 932 2 8 628-44 Fort Wood 30 03 52 -460 236 oS 50-4 56 13 26 -9 Rigolet Light 4-249 405 17 758 -45 * 89 48 15-553 265 48 58-1 85 52 32-5 Shell Point 4-060 338 11 490 -48 Grand Island 1852 30 08 49-748 191 44 45 -8 1 1 45 36-1 Point Clear 4-118 166 13 127-02 89 25 10-952 276 31 23-8 y6 37 01 -8 Bayou Pierre 4 -258 550 18 136 -35 Grand Island 1S55 30 08 58 -526 193 49 33 -5 13 50 31 -8 Point Clear 4-112 517 12 957 -37 89 25 26-S19 277 12 00-3 97 17 46-3 Bayou Pierre 4-269 285 18 590-24 Malheureux Point 30 04 24 -258 218 30 25-7 38 32 31-7 Grand Island 1S55 4-033 214 10 794 -79 89 29 37 -95S 302 54 02 '2 122 55 32-5 Nine Mile Bayou 3 -981 100 9 574-14 Martello Tower 29 56 ,39-747 192 37 33 '0 12 38 28-7 Fort Wood 4-135 271 13 654 -35 89 50 06 -982 262 13 07-3 82 16 25-8 Proctor Point 1853 4-031 75S 10 758 -66 New Orleans, St. Pat- -'9 56 45-248 275 07 42-1 95 12 04-4 Ducros 4 -I, so 739 I 14 149-44 rick's Church 90 04 1 1 -530 302 19 26-4 122 23 53 -6 Caernarvon 4 '231 066 2 17 024-18 Nine Mile Bayou 30 01 35-344 174 31 12 -I .\S4 30 47-6 Grand Island 1S55 4-137 007 13 709 -04 89 24 37-900 239 24 32 -I 59 26 .■56-1 Oyster Bayou 1855 3-886 .843 7 706-25 Oyster Bayou 1855 30 03 42-646 140 47 35-5 320 45 06-7 Grand Island 1855 4-098 857 12 556-16 89 20 .30-242 2.M 53 19-9 54 56 36-7 Bayou Pierre 4-108 621 12 841 -65 Proctor Point 1853 29 57 26 -888 147 09 48-9 327 07 25-8 Fort Wood 4-150 236 14 133-05 89 43 29-441 196 38 18 -s 16 39 29-7 Shell Point 4 -122 559 13 260 -47 Rigolet Light 30 09 13-411 255 27 45-4 75 31 35-2 East Pearl River 4-101 598 12 635 -66 89 39 04-455 300 22 34-6 120 27 18-8 Malheureux Point 4-245 179 17 586 -48 Shell Point 30 04 19-492 200 01 05-8 20 02 07 -6 Rigolet Light 3-983 750 9 632 -74 89 41 07-675 269 29 48-7 89 35 34 '3 Malheureux Point 4-266 540 18 473-11 THE MAIN TRI ANGULATION. 247 D. ADDITIONAL CxEOGRAPHIC POvSlTIONS OF ASTRONOMIC STATIONS FOR WHICH TRIANGLES ARE NOT GIVEN IN THIS PAPER AND WHICH WERE DERIVED DIFFERENTIALLY. •Stations. Maine. Banj^or , Cape Small Farmington Isles of Shoals, astronomic latitude station JMassac/im^ct/s. Cambridge, Cloverden Observatory Cambridge, Harvard Observatory Indian Sbootflying Rhode Island. Spencer New York. New York, Rutherford Observatory Dehi'cuare. Cape Henlopen Light-House, astronomic azimuth station * Dover, astronomic latitude station Dover, astronomic longitude station Rlaryland. Rockville, astronomic latitude station' , District of Cotumbia. Causten Georgetown University Observatory Seaton United States Coast and Geodetic Survey Office, transit in yard United States Naval Observatory, old site, dome United States Naval Observatory, Georgetown Heights, center of clock room Viri^inia. Charlottesville, McCormick Observatory Elliott Knob, astronomic azimuth station* Strasburg, astronomic latitude station Strasburg, astronomic longitude station North Carolina. Statesville, astronomic longituile station 35 46 54 '34 Sci 5;, 40 44 * Stations in common with and fixed by the transcoutiueutal triaugulatiou. I.atitiule. Longitude. / „ / // 44 48 14-19 68 47 01 -20 43 46 41 -24 69 50 45 20 44 40 2078 70 09 18-40 42 59 12-87 70 36 51 19 42 22 44-28 71 07 18-46 42 22 51-48 71 07 44 74 41 25 44 75 70 40 41 54 41 41 "5 '34 70 2C) 50 59 41 40 41 -25 7' 29 41 52 40 43 49 '37 73 59 ■5 'IS 3S 46 39 '42 75 05 03-52 39 09 18-59 75 31 24 56 39 09 18-59 75 3' 2a -51 39 05 09 -oS 77 09 37-20 3S 55 33 -'6 77 04 24-37 3S 54 27 -Si 77 04 39-61 3S 53 26 -82 77 00 00 -ID 3>'^ 53 10 -Ql 77 00 32 -71 3S 53 40-12 77 03 06-68 38 55 14 -89 77 04 l>2 -So 38 01 55 91 78 31 21 -15 38 09 57 '22 79 iS 5' -84 38 59 27 -Si 78 21 39 -74 38 59 27 -S2 78 21 39 -54 2^8 THE EASTERN OBUOUE ARC. Atlanta, astronomic station Stations. Georgia. A/aha ma. Lower Peach Tree, astronomic station Mobile, astronomic station Montgomery, astronomic station Louisiana, New Orleans, astronomic station of 1S5S New Orleans, astronomic station of 1880 and 1895 I,atitude. o / // 33 44 56-10 31 50 -iS'si 30 41 28 -91 32 22 37 -37 29 57 '■'^■05 29 56 51 ■51 Longitude. o / // 84 23 19-41 87 32 43 ■37 88 02 33-83 86 18 00 '92 90 04 25 -14 90 04 12 'iS E. ADDITIONAL GEODETIC AZIMUTHS COMPUTED DIRECTLY FROM THE GIVEN POSITIONS OF THE TWO STATIONS. Cape Small stations. Maine, il/nssar/niseiis. Cambridge, Harvard Observatory, dome Indian Shootfiying Spencer District of Columbia. Causten Seaton Azimuth. Back azitnuth. To stations. / // / // 155 18 59 '9 335 09 17-1 Sabattus 356 25 25-1 176 25 59 '5 Blue Hill- 135 36 02 '6 315 20 49 '5 Copecut 143 03 19-5 322 53 33 '9 Manomet 1S5 57 36-5 5 59 22-8 Beaconpole 210 54 38-3 30 59 17-2 Soper 265 32 42-33 85 37 12 -16 Hill I I PART III THE ASTRONOMIC MEASURES. 249 111. THE ASTRONOMIC MEASURES. A. RESULTS FOR LATITUDE AT THE ASTRONOMIC STATIONS OF THE OBLIQUE ARC. I . GENEKAI, STATEMENT. The area covered by the triaiigulation extending from Maine to Louisiana i.s well st:pplied with astronomic latitudes, determined by the Horrebow-Talcott method. The number of stations is 71, irregularly distributed over the arc, as maybe .seen in the general .sketch* of the location of the astronomic stations. In the northeastern half of the arc there are twice as many stations as in the other half. In some localities the stations are closely clvLstered, as in latitudes 38° 45' to 40°, and in latitudes 44° to 45°, but upon the whole a satisfactory number of fairly well distributed stations are avail- able for the .study of the local and regional deflections of the vertical. At nearly all the stations the latitude was determined with a zenith telescope. At iour stations the determination depends entirely upon ob.servations made with Air3''s Zenith Sector, f At two stations both the above instruments were u.sed, and at one of these a tran.sit in the prime vertical was also used. At a few stations ()l)ser\-ations were made with other in.struments, as stated in the abstracts of results. The results for latitude are here presented in the form used in the di.scu.s.sion of the arc of the par- allel, but for those stations which are in common with that arc the final \-alues alone are given. What has i)een said respecting instruments, observations, and method of reduc- tion of latitudes in the publication of the arc of the parallel applies equally well to the present publication, and that publication should be consulted for further details. The ob-servations used extend over the interval between the years 1S46 and 1S9S. The observations made before that time have been .superseded by the introduction of new measures, using more refined methods and .superior instruments. Some results at the Harvard College Ob.servatory and the old Naval Observatory at Washington are incorporated in the table of results. The reduction of the observations for latitude was examined with a view of improving the mean star places, and in those cases where the residual, or difference of result from any pair of .stars from the indiscriminate mean of all, was greater than 3)^ times the probalile error of the result from that pair, the mean places of these .stars were recomputed. * See Map B in pocket. t Kor di.scn.ssion of tlie result.-: obtained by ii.sing tliis in.strnnient, see .Special Pulilication No. 4. "The Transconti- nental Triangulation," XTnited States Coast andVleodetic Survey, Wa-sliington. II. C, 191x1. ■251 252 THE EASTERN OBLIQUE ARC. The method of determining mean places of stars was to abstract from all available catalogues the north polar distances and to appl>- to them such systematic corrections as were known to attach to the catalogues (principally determined by the researches of Professor Lewis Boss ) . These north polar distances were next reduced to a common epoch, usuall}' the 3"ear 1890, using the given precessional values and approximate values for the proper motion, and applying relative weights conformable to a well- proportioned system, embracing the catalogues in general. Finally the most probable corrections to the assumed north polar distances and proper motions were derived b}' application of the method of least squares; the probable errors of these quantities likewise became known. For convenience of reference the star numbers given in the abstracts are tho.se of the British As.sociation Catalogue; when not contained therein, the number in parenthesis ( ) refers to the Greenwich Ten Year Catalogue of 1880; a number in brackets [ ] refers to the Coast Survey Catalogue given in Appendix No. 7 of the Report for 1876; an asterisk attached to any star number directs attention to the fact that the star is also used in another pair or pairs at that .station. The observed component of a close double star is identified by the subscript letters P, F, and M, meaning preceding, following, or mean, respectively. Referring to the abstracts of results at the several stations the column headed "Adopted seconds of mean N. P. D." contains the .seconds of the star's mean north polar distance for the beginning of the year of observation, as adopted in the latitude computation; the column headed ;/' gives the number of observations made upon the pair; the colunni headed zc gives the relative weight assigned to the result from the pair; the last column, headed z', exhibits the residual of the result from each pair from the weighted mean of all the pairs. The probable errors and relative weights as given in the ab-stracts were determined as follows: Let ;? = the total number of observations at a station and 7/'= the number upon any pair, also /> = the number of pairs, and ^ = the difference of each individual result from the mean result from //uj/ pair, then the probable error of a single ob.servation for latitude is given by ^3 ^ o"4 55 ^^' n — p For the determination of relative weights zt- we need e.^ or the value of the prob- able error of the mean of two declinations of a pair; this may be obtained either from the catalogue mean places or more directl}- from the latitude observations themselves. The probable error c of a mean result from any pair is given by c^ ~ ~~- '-, where the vs ari.se both from errors of ob.servation and errors of declination, and are found by subtracting the particular values q)^, <^,, <^^, . . . , of which there are /> in lunnber from q) or the mean latitude of all. The probable errors e^^, e^, etc. of the latitudes <^^, ,, etc. are given by: ^^, = ^'t. + ^- <^\„ = e^-^ + — etc . , where ^^, ^r', — f' and f°=- — H- — 4- . . . ; hence the weights w become: THE ASTRONOMIC MEASURES. 253 tu. ^(^.<)"' w .= (... + Q- e,c. There are exceptional cases in which these expressions do not apph'. When a north or south star is connected after reversal of instrument, with two south or two north stars, the weight assigned to each of the two pairs or doublets so formed is two-thirds of that given by the general expression, and in case of triplets the weight is but one-half. Several stars observed on one side of the zenith maj' occur with several stars observed on the opposite side; in such a case the combination may be broken up into ordinary pairs or into doublets or triplets and the weights determined as indicated above. When a single or close zenith .star is ob.served with instrument direct and instrument reversed the expres.sion for the weight becomes 7u—{ ■ 2C' + ~ J Two values can be obtained for e".^ , one from the star catalogues 2^ , where the summation extends over the two stars of the group, and the other from the latitude observations e^ The resulting latitude t is given bv -4°, and the larger of the two values was used. (p=- and its probable error by (P .+ - . . • cC'^-\-ca^+. . . . 2. DETAILS AT .STATIONS. I. Ca/ois, Maine. — G. \V. Dean. Zenith telescope No. 4. September 2 to 29, 1S57. One division of level = I '''00. One turn of micrometer = 43"'64. Pairs of stars. .Adopted seconds of mean N. P. D. h' TV Latitude. // // / // // 6 350 *6 365 30-60 48 -27 5 3 45 11 10-09 — 69 *6 365 6 372 4S-27 13 '37 5 3 10-30 - -90 6 394 6 419 09-46 03 '35 5 5 09 -23 + 0-17 6 475 6 520 25 '14 57 '12 I 2 09 -70 -0-30 6 4S0 -6 496 45 '94 25 -32 5 3 09-25 - 0-15 6 491 *6 496 14 '34 25 '32 5 3 09 -00 — 0-40 6 547 6 555 35 -SS 13-12 3 4 09 -26 + o"i4 6 566 6 593 55 '50 17 -87 4 4 09-S9 -0-49 6 629 6 690 oS-47 16-56 2 3 08 -36 - I -04 *6 635 6 65 > 19 '32 40-97 5 3 10-27 -0-87 *6 635 6 667 19-32 58 -60 5 3 10-09 —0 -69 6 6S7 6 711 09 '55 50 -24 4 4 10 -21 — o-Si 6 721 6 745 43 '40 35 79 3 4 10-96 -1-56 6 717 *6 769 so -9S 04-90 3 2 08-54 -fo-S6 6 741 *6 769 41 -70 04-90 4 3 08-30 -fl lO t The details of the method of making and reducing astronomic observations used in the Coast and Geodetic Sur\-ey are published in the Report for 1^97-98. .Vppendix No. 7, "Determination of Time, Longitude, Ijititude. and Azimuth." 254 THE EASTERN OBLIQUE ARC. I. Calais, Maine — continuei Pairs o f stars. 6 763 *6 S17 6 764 *6 .S17 6 784 6 S47 6 S51 *6 924 *6 924 6 99S 6 944 6 994 7 060 7 131 7 062 *7 119 7 091 *7 119 7 176 7 194 7 204 7 215 7 ^41 7 268 7 277 *7 294 *7 294 7 3S3 7 301 ^^7 333 *7 333 7 345 7 365 7 3«5 7 39''' 7 4S8 7 465 7 494 7 521 7 560 *7 623 7 699 *7 623 *7 707 7 693 -7 707 *7 71S 7 72r *7 71S 7 731 *7 753 7 778 *7 753 7 7«2 7 766 *7 79« *7 79'S 7 S29 7 S15 7 880 7 S45 7 906 7 923 7' 973 7 972 7 999 8 023 "8 082 *8 028 8 059 *8 028 *8 082 8 114 8 171 8 188 *8 211 *8 211 8 268 51 60 92 *I5S *I5S 169 Adopted seconds of mean N, P. D. n' 70 Latitude. V // // 0, / // // iS -35 43-16 4 3 45 11 10-33 -0-93 45 '64 43-16 5 3 09 -90 —0-50 08 "90 00 -62 2 3 07-84 + 1-56 39 '^0 17-30 4 3 08-54 +0-86 17 '30 43-00 I I 07-45 + 1 -95 44 "21 27 -oo 2 3 09-63 -0-23 59 '69 28 -60 4 4 08 -48 , +0-92 2 1 70 09-75 6 3 08-99 +0-41 38-1. 09-75 6 3 09-65 -0-25 38 -28 00 -80 5 5 08-98 +0 -42 47-69 55 -60 4 4 09 -40 -00 39 '50 43 -00 5 5 09 -40 -00 53-13 30 76 3 2 08 -86 +0-54 30-76 41 -63 3 2 oS -67 +0-73 08 '22 27-17 6 3 09-94 —0-54 27-17 28 -33 6 3 09-92 —0-52 10 '66 47-27 6 5 10 -30 —0 -90 10-65 09-62 3 4 08-63 +0-77 54 -87 47-30 6 5 09-18 -t-O-22 37-40 42 -03 7 5 10 -43 -I -03 26 '31 30 -74 6 3 09-54 -0-14 26 -31 40 -53 3 2 10 -03 — -63 44-43 40 -53 4 3 09-47 -0 -07 22-51 28-68 3 2 10 -I I -0-71 22 -51 1 8 -35 2 2 09 -98 -0 -58 56 -34 06 -19 4 3 09-13 +0-27 56-34 31 -74 4 3 09-32 +0 -08 54-51 18 -40 6 3 09 -63 -0-23 18 -40 53-93 4 3 10 -16 — -76 10 -98 16 -71 4 4 oS-62 + 0-78 26 -22 09-07 5 5 09 -86 -0-46 31 '43 46-55 4 4 07-89 + 1 -51 48 -35 44-54 4 4 oS-70 + 0-70 29-46 27 -80 4 3 08 -56 -Ho -84 37 -47 57 -50 5 3 09-25 +0-15 37-47 27 -80 5 2 09 ■ 1 8 +0 -22 56-00 28 -62 5 5 09-46 —006 20 -70 35-97 5 3 10 -30 —0 -90 35 -97 39-86 5 3 09 -22 +0-I8 51 -52 II '75 5 5 08-63 +0-77 03 -53 16 -JJ 4 3 09-71 -0-31 lb -41 5I-.S5 ,<> 3 09-92 -0-52 Indiscriniiiiate me -•:i=45'' 11' 09" -38. Weighted mean --J5 1 : 09 -4od[zO' '•67. '-06. 243 observatiori.s, ^ --.•] pairs. llledii'-tiou tc /L=o "•oc.? THK ASTRONOMIC MEASURES. •^0 2. Cooper, Maine. —E. Goodfcllow. Zenith telescope No. 5. September S to 18, 1859. One division of level =0" "96 from observations at this station. One turn of micrometer=4i''' '416 from circumpolar observations at this station. Pairs of stars. 6 365 6 372 6 404 6 428 6 473 6 476 6 497 6 5(X) 6 491 6 496 6 542 6 586 6 602 6 612 6 657 *6 662 *6 662 6674 *6 662 6 676 6 730 *6 817 6 734 *6 S17 6 857 6 895 *6 930 6 940 *6 930 6 943 *6 957 6 970 *6 957 7 024 *6 957 7 051 7 060 7 131 7 152 *7 176 *7 176 7 194 7 213 7 262 7 26S *7 333 7 301 *7 333 7 42S 7 444 7 455 7 477 7 501 7 503 7 533 7 56S 7 595 7 607 7 611 7 627 7 693 7 708 7 721 *7 749 7 731 *7 749 7 789 7 798 7 803 7 845 7 8S0 7 888 7 913 7 950 A(loi)te(l s int-aii N sconds of . P. D. n' IV Latitude. V // II / // II 42-25 06-93 6 12 44 59 13 -06 — 046 28 w 32 -64 6 12 12 -42 + 0-18 33 ■20 54 -70 6 12 12-55 +005 57-59 04 -66 4 9 12 -20 +0-40 05 -02 '5-97 2 6 13 35 -0-75 54 •"'> 26-25 5 II 12 -24 +0-36 30-86 II -47 5 II 13-02 —0-42 19-92 24 -50 5 5 12 -98 -0-38 24-50 04-41 6 6 II -97 +0-63 24-50 09-87 6 6 12 -04 + 056 33 -80 25-32 6 8 12 21 + 0-39 14 -20 25-32 6 8 12-03 +0-57 32 -78 10 "09 6 12 12-75 -0-15 55-22 40 -40 6 8 12-67 —0 -07 55-22 32-27 6 8 12 -70 — 010 48 -49 51 -27 6 6 12 -21 -to -39 48 -49 22 -70 6 6 II -88 + 0-72 48-49 19-74 6 6 13 -05 -045 36-32 04 -62 4 9 12 -10 + -.50 27-25 12-79 6 S 12-66 — 0-06 12-79 35-04 6 8 12-37 +0-23 3' -52 21 -73 6 12 12-44 + 0-16 15 -44 58 -81 6 8 13 -oS — O-4S 40-50 58-81 6 8 12 -Si —0 -21 30-58 49-10 6 12 12-48 -fO-12 41-58 38 -88 6 12 13-11 -0-51 12-63 48-21 5 II 12 19 +0-41 03-43 33-26 6 12 12-65 — 005 44-38 .=io -73 6 12 II 92 +0-6S 06 -91 12-34 6 12 12 -34 +0-26 09-71 19-01 6 12 13 -35 -0-75 53-76 34 -68 6 8 13 -02 -0-42 43-18 34 -68 6 8 13 19 —0 -59 06-30 42-31 6 12 12 32 +0-2S 50-58 49 -58 5 II 13 -00 —0 -40 39 -73 54-17 6 12 13 -39 -0-79 39 -83 3 1 -60 6 12 12 "22 +0-38 scriminate mean = 44" 59' 12" 59. jhted me; ui =44 59 12 -603:0" -05- -52. 209 ob.servations, 37 pairs. [Reduction to J^ = -r o" -04.] 3- Hiitnpback, Maine division of level = 0'' -66 station. Pairs of stars. 5 628 5 677 5 747 5 So I 5 SS6 *5 937 5 S95 *5 937 5 990 5 997 6 013 6 109 6 246 •■6 349 6 25S *6 349 6 364 6 428 6 404 6 476 6 497 6 500 6 553 6 601 6 697 6 711 6 731 *6 754 *6 754 6 779 6 817 6 S95 6 930 6 943 6 957 6 970 6 9S5 7 022 *7 062 7 lOI *7 062 7 i'4 7 152 7 176 7 204 7 281 7 306 7 3'7 7 39S 7 44S 7 469 7 477 7 4S9 7 505 7 533 ^7 568 *7 542 7 623 *7 542 '*7 56S 7 683 7 721 7 731 7 749 7 789 7 79S 7 «43 7 S48 7 8S0 7 888 7 913 7 950 7 999 8 023 THE EASTERN OBLIQUE ARC. -A. T. Mosman. Zenith telescope No. 5. July 26 to August 19, 1858. One One turn of micrometer = 41" '416 from circumpolar observations at this Adopted mean seconds of N. P. D. n' rt' I.atitude. V // // / // // 28-68 07 -80 8 13 44 51 47-33 + 0-23 24 73 02 -21 8 13 47-32 + 0-24 14 -84 31 'oo S 9 48 -28 —0-72 10 '07 31 -GO 7 9 47 -16 + -40 57 '91 28-45 8 13 46-99 + 0-57 06 ■91 24-09 8 13 47-23 + 0-33 46 -63 07 -40 8 9 47-78 — -22 58 '60 07 -40 8 9 47-68 — -12 34-31 36 -50 5 12 47-40 + 0-16 31 -92 59 -oo 5 12 48 -II -0 -55 02 -32 rig -46 8 13 47-28 + 0-28 10 -36 19-83 8 13 47-30 -fo-26 16-63 42-70 8 13 47-43 H 0-13 01 71 36 -42 8 9 47-60 —0 -04 36-42 50-04 7 9 47-03 -fo-53 34 -24 19-90 8 13 47-70 -0-14 05 -46 42 -80 10 14 47-66 — o-io 59-05 02-73 8 13 46-76 +0 -80 12 -07 44 -87 8 13 47-17 +0-39 09 -98 37 -80 9 9 47-28 +0 -28 09 -98 22 -64 9 9 46-88 +0-6S 39 -50 25 -53 10 14 47-64 —0 -08 34-47 28-63 9 14 47-24 +0 -32 01 -42 03 -81 8 13 47 -58 —0 -02 55 -77 07 -85 8 13 47-94 —0 -38 00-53 54-45 8 13 47-93 -0-37 20 -09 03 -20 8 13 48-04 -0-48 19 '60 49-35 9 9 47-30 -fo-26 27-70 09 -63 8 9 48-18 — 0-62 2770 49-35 7 6 47-54 +0-02 01 -20 II -22 8 13 48 -40 --0 -84 00 73 52-37 9 14 48-13 -0-57 24 -3 1 m -34 9 14 47-50 +0 -06 10-59 38-90 6 12 47 -56 -00 58-30 12-75 8 13 47-80 —0 -24 58-56 50-46 9 14 47-24 +0-32 25-40 io-i8 8 13 48 -lo -0-54 criminate mean = 44° 51 ' 47"-55- hteil mean = 44 51 47 -56 : t o"-o5. C = ±o"-- )6. 296 observations, 37 pairs. [Reduction to A = — 0^^-43.] i THE ASTRONOMIC MEASURES. 25; 4. Bangor, Maine. E. Goodfcllow. Zenilli telescope No. 5. Septeml One division of level =o''''S6. One turn of micrometer =4i'''''397- er 7 to October 10, 1S.57. I 'airs stars. 6 427 6 477 6 496 6 497 6 500 6 534 6 579 6 593 *6 697 6 711 *6 697 6 765 6 771 6 824 6 849 *6 881 6 S60 *6 881 6 930 6 944 6 959 7 001 7 027 *7 062 *7 062 7 114 7 171 7 219 7 233 7 253 7 290 7 306 7 398 7 448 7 455 *7 477 *7 477 7 480 7 488 7 505 7 548 7 565 7 623 7 708 *7 668 7 721 *7 668 7 731 *7 727 7 743 *7 727 7 770 7 749 7 843 7 S75 *7 914 *7 914 7 973 7 999 S 023 8 059 *S 118 8 082 *8 118 8 126 8 171 8 279 *8 374 8 33S "•8 374 46 log So 164 *254 310 *254 321 263 335 395 450 Adopted .seconds of mean N. P. D. // // 4f) 'So 38 -79 25 -33 "7 -"5 14 -26 59 -63 43 '94 ■7-87 24 ■ 1 1 50-24 24-11 01 -cS3 19 63 24 -22 27 -82 05 -78 27 "48 05 -78 '570 44-21 54 '82 30 -58 45 "2o 21 96 21 -96 34 -80 44 19 38-12 52 -89 08 -96 01 32 15 -33 10 '65 23-15 12 -40 10 -02 ID '02 iS -72 09 '62 19-17 53 '03 50-24 26-31 53 -84 30-54 28 -68 30 '54 18 -35 54 '43 17-33 54 '43 14-68 09-97 28 -90 35 '6' 15 -26 15 -26 46 -55 44-54 29-46 57 -50 23 -82 27 -So 23-82 07-92 28-62 47 -87 03 -23 06 -88 03 -23 42 -28 13-48 42-58 54 -68 32 '53 04 -91 32 -53 07 -83 31 -24 33 -09 19-90 41 -40 10 7 7 10 7 7 10 6 6 10 10 7 7 10 10 10 10 7 6 10 10 ID 6 7 5 6 10 6 7 10 6 7 10 7 7 10 10 5 5 8 10 44 48 ide. I -88 ■ 99 3 -07 —0 20 2 -02 - -8.5 2 -27 ^0 -60 3-07 — 020 2-55 4 -32 3-45 -0 -58 2-68 - -19 2-91 -0 -04 2-85 ro 02 3-'i —0-24 2-93 06 2-34 -0 -53 2 99 —0-12 2-80 — 07 2-46 ■4-0-41 3-23 —0 -36 3 -54 —0-67 2-62 4-0-25 2 -21 -I-0-66 1 -97 —0 -90 3-17 —0 -30 3 39 -0-52 3-31 -0-44 3 -21 -0 -34 3-36 -0-49 2-37 —0-50 3 "02 -0-I5 2-78 +0-09 3-07 — 020 2-71 -0-16 3-44 -0 -57 3-89 — I 02 3-82 -095 3-19 -0 -32 3 ->9 —0 -32 3 -00 --0-I3 3 -'3 —0-26 2-67 -rO-2o 2-70 -rO-I7 2 -27 ~-o -60 4193 — No. 7- Indiscriminate niean=44° 48' i2"-9o. Weighted moan =44 48 12 -87^:0" -05. ,.= ±o"-3S. 213 observations, 41 pairs. [Reduction to A=o"-co.] — 17 258 THE EASTERN OBLIQUE ARC. 5. Fariiih/g-/oi/, Maine. Oue division of level = o''' C. O. Boutelle. Zenith telescope No. 5. October 8 to Noveml)er 6, 1866. 90. One turn of niicronieter = 4i^''48. Pairs of stars. 6 599 6 697 6 723 6 806 6 824 6 875 6 928 6 937 6 973 7 024 7 091 7 114 7 233 7 241 7 253 7 306 7 36« 7 3S7 7 444 7 449 7 474 7 482 7 524 7 560 7 627 7 700 ^ 746 7 765 7 S45 7 850 7 888 7 901 7 950 7 9S3 7 994 8 059 S 037 8 082 S 114 8 118 8 159 8 188 8 212 8 231 8 279 8 284 4 46 67 83 158 201 244 2S5 314 334 425 441 492 540 610 647 691 7(X) 721 786 Adopted mean seconds of N. P. D. «' n // 12 -Q 167 5 56-4 34-6 5 03 '5 237 6 45 '5 II -Q 7 42-6 03-2 7 51 -o 44 '6 6 54-2 38-6 6 08 'o 10-4 6 16 -6 16 -Q 6 03 -6 51 "5 6 48-6 30-0 6 04-6 157 6 15-4 27-4 8 167 57 '4 8 41 "5 46 -o 7 44 7 46-8 7 21 -5 46 -o 5 37-6 01 -Q 6 51 7 31 '5 6 00 'o 27-4 5 02-5 22 -S 6 07 "O 12-6 7 48-0 II -o 6 57-5 42 -Q 6 25-1 46-5 6 i8-o 467 6 14 'O 55-6 6 187 26-5 6 18 -4 06-3 6 48-4 23 'O 5 51 "4 107 5 56-0 09 '5 5 II -6 55 7 5 w Latitude, V / // // 5 44 40 19 '49 +0-05 5 19-85 -0-31 6 19-40 +0-I4 6 20 -06 -0-52 6 1879 +0-75 6 19-27 +0-27 6 19-78 -0-24 6 19-40 +0-14 6 19-09 +0-45 6 19 '05 +0-49 6 19 "26 +0-2S 6 19-97 -0-43 6 19 -01 +0-53 6 18-37 + 1-17 6 19 "57 -0-03 6 20 -17 —0-63 5 20 -29 -0-75 6 19-27 +0-27 6 19 -02 +0-52 5 20-38 -0-S4 6 19 '43 -t-o-ii 6 19-27 +0-27 6 19-70 —0 -16 6 19 '52 -fo-02 6 20-07 -0 -53 6 18-67 +0-S7 6 19-77 -0-23 6 18-96 +0-58 6 1973 —0 -19 5 18 -64 +0-90 5 19 -00 +0-54 5 19-70 —0-16 5 19 '55 — O-QI THE ASTRONOMIC MEASURES. 259 5. Fann!)if{lo)i, Maine — conliiiue'l. % Pairs f stars. Adoptee mean seconds of N. P. D. n' 7V Latitude. V /r // / // // 6 930 6 944 43 "4 07 '5 7 6 44 40 20 -06 -0 52 6 996 7 062 03 36-2 8 6 19 46 -o-o8 7 o'^S 7 101 51-6 cxj '5 6 6 19 57 —0 -03 7 17' 7 254 50-0 28-6 s 6 19-91 -037 7 278 7 3'3 05-6 06 'O 7 6 '9-35 -ho -19 7 365 7 373 00 'O 05 -o 7 6 19 45 +0-09 7 399 7 401 51 'o 53 'o 6 6 18-26 + 1 -28 7 469 7 477 57-0 50-0 6 6 20 -23 —0-69 7 4SS 7 505 47-8 56-0 7 6 19 "45 -fo-09 7 548 7 554 27 '5 07 '2 6 6 2o-i8 —0-64 7 565 7 598 22-5 35 "o 7 6 18 -86 +0 -68 *7 668 7 721 55 7 52-5 6 4 19-96 -0-42 *7 668 7 73' 55 7 43 'o 5 4 19 -10' -fo-44 7 753 7 813 18 -8 50-1 6 6 18-86 +0 -68 7 S55 7 9>5 20 -6 25-8 6 6 19 '59 — 005 7 958 7 967 18 -5 14-2 6 6 19-29 -rO-25 8 023 8 126 36-0 10-5 6 6 19-88 -034 8 158 8 211 59 '3 36-0 7 6 18-66 4-o-SS 8 224 8 237 03-5 28-0 6 6 19-51 +0-03 52 79 44-5 22 '2 6 6 20 --2 —0-48 173 232 37-6 22-8 6 6 20 -57 -1-03 239 299 44-1 19-5 6 6 20-36 -0-S2 395 450 27 -o 52 -s 6 6 ■9 '36 +0-IS 5S8 630 56-3 43-3 6 6 iS-26 + 1 -28 668 679 21 -6 45-2 6 6 20 -Sr -I -27 705 727 03-8 48-5 6 6 19 '54 -00 785 87. 31 -o 05 -o 5 5 20-58 -I -04 962 963 04 '5 46-5 5 5 20 -76 — I -22 981 995 00 'O 44-4 5 5 20 -58 -I -04 I 006 I 083 12-6 01 -3 6 6 iS-49 -f-I '05 I 129 I 139 39 'o 51 '5 6 6 20-02 -O-4S I 219 I 254 49 7 57-5 6 6 20 -42 -o-SS Indiscriminate mean Weighted mean e 397 observations, 65 [Reduction 44° 40' =44 40 ==to"-55 Dairs. to ^ =0" i9"-55. 19 •54±:o""05. •00.] 26o THE EASTERN OBLIQUE ARC. 6. iMouiit Harris, Maine. — G. W. Dean. Zenith telescope No. 2. First series. August 15 to 24, 1S55. One division of level =i"'i6. One turn of micrometer =44'''8o3 from circumpolar obser- vations at this station. Pairs of .stars. Adopted seconds of mean N. P. D. n' w I^atitiide. 7' // // / // // 5 S40 5 922 35 '25 36-72 5 II 44 39 54 -25 + 0-44 6 129 6 218 26^04 05 -44 5 II 55-20 -0-51 6 232 6 3fi 37-00 04-40 3 9 54-88 — 0-19 6 237 6 318 2470 48 -24 3 9 54-32 + 0-37 6 335 6 394 30-40 16 -96 3 9 54-12 + 0-57 6 372 6 ,392 19 -81 38-24 2 7 55 -08 -0-39 6 419 6 466 10-93 58-34 5 II 55-07 -0-38 *6 477 6 497 47-66 16-62 3 6 54-04 + 0-65 *6 477 6 553 47-66 25-85 2 5 55-18 -0-49 ^6 623 6 651 51 -94 54-43 5 7 54-43 +0-26 *6 623 6 667 51 -94 12-59 5 7 53 -95 +0-74 6 711 6 723 05 '36 21 -21 5 II 54-92 -0-23 6 731 6 754 25 -28 00 -98 5 II 54-82 -0-13 6 824 6 875 42 -20 09 -08 5 II 54-73 —0-04 6 92S 6 937 41 -81 05-18 6 II 54-45 +0-24 6 973 ■'7 024 40-25 08-02 6 7 54-11 +0-58 6 978 *7 024 03 -28 . 08 -02 4 7 55-01 -0-32 7 062 ■■'7 114 45-20 58-23 5 7 53 -98 +0-71 7 091 / 114 02 -02 58 -23 5 7 54-62 +0-07 7 233 7 241 19 -18 06 -ID 5 II 54-90 — -21 7 253 7 306 35 -81 43-49 5 II 54-92 -0-23 7 368 7 3S7 56 -50 58 -31 5 II 54-36 +0-33 7 399 7 401 35-19 36 -22 5 II 54-30 +0-39 7 469 7 477 46 -90 41 -iS 4 10 55-64 -0-95 7 488 7 505 41 -12 50-84 5 II 55-31 —0-62 7 524 7 560 00 -92 14-76 5 II 55-47 -0-78 7 571 *7 61 1 10-83 13-60 5 7 54-19 +0-50 7 584 *7 611 58 -95 13-60 5 7 54-20 +0-49 7 651 7 693 43 -49 18 -07 5 II 54 -98 —0 -29 7 746 7 765 30-45 12 -20 5 II 54-22 +0-47 7 845 7 850 02-93 07-71 5 II 54 -86 -0-17 7 9*52 *7 999 47 -80 22-81 3 6 55-14 -0-45 *7 999 8 023 22 -Si 08 -00 2 5 55-49 -o-8o 8 037 8 082 24-29 06-94 4 10 53 -83 +0-86 8 114 8 128 35-50 53 -70 5 1 1 54-72 —0 -03 8 156 *8 188 55-49 00-36 5 7 54-44 +0-25 8 159 *8 188 39-44 00-36 5 7 54-79 —0 -10 8 212 8 231 45-25 5' -97 5. II 55-08 -0 -39 8 237 8 261 06-22 04-35 5 II 54-33 +0-36 8 279 8 284 I 27-94 ndiscriminate 51 -44 mean = 4 =44° 39' 54 10 ''-68. 54-81 —0-12 A Veighted mean = =44 39 54 -69^ =0^^-05. e- = ±o"-37. I 79 observations, 40 pai rs. THE ASTRONOMIC MEASURES. 261 6. Moinil Harris, Maine. — G. W. Dean. Zenith telescope N 27. 1855. One division of level =0" '632, from observations at meter =39" '522 from circumpolar observations at this station. o. 10. Second series. August 6 to this station. One turn of tnicro- rains of stars. 5 731 5 797 5 Ho 5 922 5 944 6 036 6 129 6 21S 6 232 6 31 1 6 237 6 31S 6 335 6 394 6 372 6 392 *6 419 6 456 *6 419 6 466 *6 477 6 497 *6 477 6 553 6 566 6 581 *6 623 6 651 *6 623 6 667 6 711 6 723 6 73> 6 754 6 824 6 875 6 92S 6 937 6 973 *7 024 6 978 *7 024 7 062 *7 114 7 091 *7 'H 7 233 7 241 7 253 7 306 *1 368 7 377 *7 368 7 387 7 399 7 401 7 469 7 477 7 488 7 505 7 524 7 560 7 57' *7 611 7 584 *7 611 7 651 7 693 7 746 7 765 7 789 7 798 7 S45 7 850 7 879 *7 888 7 880 *7 SSS 7 9'3 7 950 7 962 *7 999 *7 999 8 023 8 037 S 0S2 Adopted seconds of mean N. r. I). 71 ' IV Latitude. V // // / // // 25 '48 26-99 5 16 44 39 54 -99 -0 -48 35 -25 36-72 6 [7 54-13 +0 -3cS 05 -ss 09 -54 5 16 54-37 -}-o-i4 26 '04 05 -44 5 16 54 -66 -0-15 37 -dO 04 -40 5 16 54-81 -0-30 24 •70 48 -24 4 15 54-41 + ID 30 •4() 16-96 3 '4 54-61 — 010 19 -Si 38-24 2 1 1 54-52 — Q-OI 10-93 24 -22 5 II 55 -38 -0 -S7 10 '93 58-34 5 II 55-15 —0-64 47-66 16-62 5 1 1 53 -65 +0 -86 47-66 25 -85 5 II 54-76 -0 -25 05 -37 03 -90 5 16 54 -84 -0-33 51 94 54 -43 5 II 54-77 —0 -26 51 '94 12-59 5 II 54-70 —0 19 05 '36 21 -21 6 17 54 -73 —0 -22 25 -28 00 -98 6 17 54-19 +0-32 42 -20 09 -08 6 17 54 -36 +0-15 41 -81 05 -18 5 16 54-44 + 0-07 40-25 08 -02 6 II 54-63 —012 03 -28 oS "02 6 u 55-01 — o-5» 45 '20 58 -23 6 II 53-97 +0-54 02 -02 58 -23 6 II 54 -38 ^0-13 19 -iS 06 "lo 6 17 54-18 +0-33 35-8. 43-49 5 16 54-58 — 007 56 •5<-> 31 -10 5 11 54-24 +0-27 56-50 58-31 5 II 54 -29 -fo-22 35-19 36 -22 5 16 54 -05 +0-46 46-90 41 -1.8 6 17 54 57 -006 41 '12 50 84 6 17 54 -79 -0 -28 00 -92 14-76 6 17 54-69 —0 -iS 10 -83 13 -60 6 1 1 54 -22 -fo-29 58 -95 13 -60 6 II 54 -37 ~o-i4 43 -49 18-07 6 '7 54-76 -0-25 30 -45 12 20 5 16 53 -77 +0-74 18-05 53 '50 5 16 54 43 -o-oS 02 -93 07-71 4 15 54-12 -^ -39 16 69 08 -20 3 9 54 -48 - P 05 54 02 oS -20 2 8 54 -34 -0-17 54-44 46-74 5 16 54-41 +0M0 47 -80 22 -81 5 II 54 -85 -0 -34 22-81 oS -ix) 5 II 55 -34 -0-83 24 -29 06 -94 5 16 54-11 -fo -40 262 THE EASTERN OBLIQUE ARC. 6. Alount Harris, Maine. Second series — continued. Pairs of stars. .Adopted seconds of mean N. P. D. n' w Latitude. V // // / // // 8 114 8 128 35 "50 53-70 5 16 44 39 54 -83 -0-32 8 156 ''8 188 55-49 00-36 5 II 54-23 + 0-28 8 159 -'8 188 39 '44 00-36 5 II 54-69 -0-18 8 212 8 231 45 '25 51 -97 5 16 54-41 +0-10 S 237 8 261 06 -22 04-35 5 16 54-20 to -31 8 279 8 284 27-94 51 "44 5 16 55-13 —0 -62 Indiscriminate mean =44° Weighted mean =44 f=d=o 248 observations, 49 pairs. // 39' 39 29. 54'' 54 -52 -51 zbo'^ -04. 6. Mount Harris, tisane. — E. Goodfellow. Zenith telescope No. 10. Third series. September 12 to 25, 1S55. One division of level=o"-632. One turn of micronieter=39"-507 from circumpolar observations at this station. Pairs of stars. Adopted seconds of mean N. P. D. ?i' yj Latitude. V // // / // // *6 419 6 456 10-93 24 -22 I 2 44 39 54 -74 -fo-05 *6 419 6 466 10-93 58 -34 I 2 54-09 +0-70 *6 477 6 497 47-66 16-62 5 6 54-17 +0 -62 *6 477 6 553 47-66 25 -85 5 6 55-24 -0-45 6 566 6 581 05 -37 03-90 6 9 55-02 -0-23 *6 623 6 651 51 -94 54 -43 6 6 54-86 —0 -07 *6 623 6 667 51 -94 12-59 6 6 54 -74 +0-05 6 711 6 723 05-36 21 -21 5 9 54-43 +0-36 6 73T 6 754 25 -28 00-98 5 9 55-50 -0-71 6 S24 6 875 42 -20 09-08 6 9 54-74 +0-05 6 928 6 937 41 -81 05-18 6 9 54 -45 +0-34 6 973 ^7 024 40-25 08 -02 6 6 54-42 +0-37 6 978 *7 024 03 -28 08 -02 6 6 54-30 +0-49 7 062 7 114 45-20 58 -23 6 9 54-88 —0 -09 7 233 7 241 19-18 06 -10 6 9 53-74 + 1 -05 7 253 7 306 35 -81 43 '49 6 9 55-44 —0-65 *7 368 7 377 56 -50 31 -ID 5 6 54-12 +0-67 *7 368 7 387 56-50 5^-31 6 6 54-59 +0-20 7 399 7 401 35-19 36 '22 6 9 54-37 + 0-42 7 469 7 477 46 -90 41 -18 6 9 55-30 -0-51 7 488 7 505 41 -12 50-84 6 9 55-45 -0-66 7 524 7 560 00 -92 14-76 6 9 54-91 —0-12 7 571 *7 611 10-83 13-60 4 5 54-66 +0-13 7 584 7 611 58-95 13-60 7 6 54 -59 -l-o -20 7 651 7 693 43 -49 18 -07 6 9 55-02 -0-23 7 746 7 765 30-45 12 20 6 9 53-80 +0-99 7 789 7 798 18-05 53 -50 6 9 55-03 — -24 7 845 7 850 02-93 07 -71 6 9 54-88 —0 -09 7 S79 *7 888 16 -69 08 -20 3 5 55-09 —0-30 THE ASTRONOMIC MEASURES. 263 6. Moiinl Harris, Maine. Third series — conlinue'l. Pairs of stars. .\do])tc{l secoiuls of mean N. P. U. n' VJ I ,;iti tilde. V // // / // ff 7 SSo *7 S88 54 -02 08 -20 3 5 44 39 55-47 -0-68 7 9'3 7 950 54-44 46-74 6 9 55-00 —0-21 7 962 *7 999 47-80 22 •8r 6 6 55-23 —0-44 7 999 8 023 22 81 08 -oo 6 6 55 -92 -I -'3 8 037 8 082 24 29 06 94 6 9 54-37 -1-0-42 S 114 8 1 28 35 "50 53 -70 6 9 55 -28 -049 8 156 *8 188 55 -49 00-36 7 6 54-47 +032 8 159 *8 188 39-44 00.36 6 6 54-90 —0 -II 8 212 8 231 45 -25 51 "97 5 9 54 -89 — 010 8 237 S'26r 06 -22 04-35 6 9 53 -80 +0-99 8 279 8 284 27-94 51 -44 6 9 55 -38 -0-59 Indiscriminate mean = 44° 39' 54" ■78. Weighted mean = 44 39 54 -79 =b 0" ■05 c = ± 0" -44. 21 8 observations , 40 pairs. Collcclion of rcsulls at station, Mount Harris, Maine. G. W. Dean, Z. T. No. 2

<' 7 368 23-23 41 -98 6 27 06 -40 4 -u 7 416 7 461 25 -02 59 -25 6 27 06-57 —0 06 7 521 7 54« 52-76 09-52 6 27 06 -42 -^ -09 7 569 7 595 20 -84 33 -83 6 27 06 -91 —0 -40 7 615 7 623 50 -84 43 -"4 6 27 06-68 -0-17 7 72" 7 754 46-19 32-42 6 27 07-04 -0-53 7 731 7 77S 35-83 24-41 7 32 06 99 -0-48 7 800 7 803 14-36 44-64 5 23 06-72 —0 -21 7 855 *7 858 24 -55 35-05 6 18 06 -80 —0-29 *7 S58 7 8S2 35 -05 26-94 7 21 06 -30 -0 -21 7 S94 7 9'3 52-06 34-79 6 IS 06 -02 + 0.49 8 141 8 1 88 32-05 40 -54 5 23 06 -99 -0-48 8 284 8 344 31 -40 44 -73 6 27 06 -60 —0 -09 S 366 8 374 17 -12 22 -62 7 32 06-44 +0-07 Indiscriniiiiatt' mean = 44 ° 2 ' 06" -48. We l^lited tiieaii = 44 2 I 06 -5 1 d= " -03. e = d= 0" ■46. 189 observati ons, 32 pairs. [Reduction to A = "-SS.] 8. Mount Desert, Maine. — E. Goodfellovv. Zenitli telescope No. 5. Second series. September iS to October 5, 1856. One division of level = o" -716 from observations at this station. One turn of micrometer = 4i'''-42i from circumjwlar observations at this station. Pairs of stars. *6 255 *6 255 6 395 *6 429 6 553 6 629 6 687 *6 769 *6 769 6 849 6 268 6 ,',57 *6 429 6 522 6 583 6 637 6 722 6 799 6 830 6 865 doptetl seconds of mean N. P. U. 1/ " 57 -91 07 -44 57 -91 23-53 18 -80 06 -94 06 -94 47 -75 20-45 05 -45 14-87 38 -62 16 -61 23 -34 14 -17 48-16 14-17 17-70 37-00 58 -58 w Latitude. V / // // 5 44 21 06-25 i-0-2S 5 06 06 +0-47 5 05 -68 +0-85 5 06 06 +0-47 8 06 97 -044 8 06 22 +0-31 8 05-63 +090 5 06 55 — 002 5 06-43 +o"io 5 06-55 —0 02 266 THE EASTERN OBLIQUE ARC. S. Mount Dcacii, jNIaine. Second series — continued. n • f . Adopted seconds of „, .,, Tot;f,.Ho Pairs of stars. „,^^„ j^ p j^ n m I.atUude, 6 S79 6 932 30-59 18 -37 7 8 44 21 06 -61 -0-08 6 979 6 994 II -65 38 -32 6 S 05-77 +0-76 7 022 7 062 07-50 33 '49 6 8 06 -66 -0-13 7 073 7 '53 24-90 42 -S3 5 7 06 -78 -0-25 7 2J9 7 253 51 ■17 22-37 4 7 07 -32 -0-79 7 220 7 256 10 -37 ]6 -II 4 7 06 -14 -fo-39 7 310 7 368 23 '23 41 -98 6 8 06-42 +0 -11 7 416 7 461 25 -02 59 -25 6 S 06 -09 + 0-44 7 521 7 548 52 -76 09 -52 6 8 06-73 —0 -20 7 569 7 595 20 -84 33 -83 6 S 07-23 -0 -70 7 615 7 623 50-84 43-04 7 8 06 -07 -+0-46 7 721 7 7,S4 46-19 32 -42 6 8 07 -II -0-58 7 731 7 778 35 -83 24-41 6 8 07 -39 -0-86 7 Soo 7 803 14 -36 44-64 4 7 07-73 — I -20 7 S55 *7 858 24 '55 35 -05 6 5 06 -20 +0 -33 7 S58 7 882 35 '05 26-94 6 5 06 -00 +0-53 7 S94 7 913 52 -06 34 -79 6 8 06 -73 —0 -20 S 141 8 J 88 32-05 40-54 6 8 07 -32 -0-79 S 2S4 8 344 31 -40 44-73 6 8 06 -21 ^ 0-32 S 366 8 374 17-12 22 -62 4 7 06 -19 +0-34 Indiscriminate mean = 44° 21' 06" -50. Weighted mean = 44 21 06 0" -41. -53 =b 0" -07. 171 observations, 30 pairs. [Reduction to A = — i" 88.] 9. Ragged Moi()!ta!)i,Ma.me. —G.y^. 'DcslU. Zenith telescope No. 5. First series. August 18 to September 7, 1854. (Jne division of level =o''-7i from ob.servations at this station. One turn of micrometer = 41^-426 from circumpolar observations at this station. Pairs of stars. 5 596 5 617 5 795 5 847 5 874 5 911 5 922 5 978 6 006 6 030 6 052 6 082 6 177 6 223 6 241 6 316 6 395 *6 429 -6 429 6 522 6 534 •■■6 583 6 659 6 711 6 734 6 806 Adopted seconds of mean N. P. D. 02 -60 50-57 14-25 JO -82 45 -86 55-20 33-71 47 -28 30-72 40-79 57 -22 39 -45 04 -82 40 -99 08 -99 36 -74 25-72 14 -28 14-28 58 -88 16-49 17-41 44 -88 12 -92 54-74 18 -22 n' ~u Latitude. ■ V / // // 2 9 44 12 43 -02 —0 -ID 4 10 43-17 -0-25 5 10 43 -45 -0 -53 5 ID 43 -50 -0-58 6 II 42-12 +0 -80 6 I I 43-51 -0-59 6 II 42-94 —0-02 6 II 42-47 +0-45 6 7 43 -01 —0 -09 5 7 42 -65 +0-27 5 7 42 -26 +0-66 6 II 42-90 +0 -02 5 ID 42-47 +0-45 THE ASTRONOMIC MEASURES. 267 9. Ragged Mounla in, Maine. First series — continued. Pairs of stars. Adopted seconds of mean N. P. D. n' w Latitude. V // // / // // 6 763 6 813 42-42 03-10 6 II 44 12 43-14 — 022 6 S24 6 9'5 51 -20 37 '67 5 7 43-25 -0-33 *6 915 6 928 37 '67 52 -oi 5 7 43 ''2 — 0-20 6 940 7 024 3' '54 '9 '33 5 10 43-45 -0-53 7 09S 7 126 44 '25 36-50 6 II 43-11 -0-19 7 "71 7 253 22 17 49 -23 6 II 42-71 ^0-2I 7 278 7 336 50 -85 57-30 6 II 42-84 ^o-o8 7 385 7 448 32-98 09-03 6 II 43 65 -0 73 7 512 7 566 03 -20 58 -74 6 1 1 42 -82 +010 7 595 7 623 06-75 16-38 6 1 1 43' 14 — 022 7 679 7 695 1974 29 -98 6 II 42-41 -0-51 7 721 7 754 21 -09 07-98 6 II 43 '32 —0-40 7 731 7 778 10 96 00-03 6 II 43-56 —0-64 7 894 *7 983 29-04 34-41 5 7 42 -75 -0-17 7 913 *7 983 13-08 34-41 5 7 42-41 +0-51 5 828 5 840 08-28 31 -00 4 10 41 -84 + 1 -08 5 900 5 972 29 -61 20-83 4 10 42-27 -0-65 6 056 6 062 51-88 00 -75 3 10 42-92 000 6 068 6 129 43 '58 26 00 3 10 42-80 -r 12 6 079 6 178 10 -S3 40-90 2 9 42-65 +0-27 6 234 6 318 41 -27 50-48 5 10 43 09 -0-17 6 238 6 311 46-34 06-55 5 10 43 "30 -0-38 6 477 *6 571 52-10 26-74 2 6 42-84 -0-08 6 496 *6 571 39-21 26-74 2 6 43 "43 -0-51 6 497 ■=^6 583 21 -36 17-41 2 6 43 '33 — 0-41 6 6S7 6 722 30 -87 38-90 4 10 42 49 -0 43 6 740 6 867 49-65 34-41 4 10 42 -82 -hO-IO 6 926 6 975 33 73 45 -95 5 10 43 '53 — 061 6 986 7 076 04 -20 54-08 5 10 43 -02 —0 -io 7 048 7 085 29 -07 13-97 5 10 43 '3' -0-39 7 243 7 337 2975 02 -50 4 10 41 -49 -^1-43 7 569 *7 615 53 '44 24 -00 I 4 43 -22 -0 -30 7 570 *7 615 04-44 24 -or; I 4 42-67 - -25 7 782 7 843 25 30 24-04 5 10 43 '45 -0-53 *7 855 7 879 01 -25 34 -92 5 7 42-52 —0 -40 *7 855 7 8S0 01 -25 12 -50 5 7 42-70 -^0. 22 Indiscriminate mean = 44° 1 2' 42"-92 Weighted mean = =44 12 42 -92 ±o"-o5. <'= :± o"-25. 228 observatiotis, 49 pa irs. [Red uction tO:^ = +o'''-40.] 268 THE EASTERN OBLIQUE ARC. 9. Ragged J\/o!i)itai II, Maxna. — S.Harris. Zenith telescope No. 5. Second series. September ir to October 6, 1854. One division of level =0" 77 from observations at this station. One turn of micrometer =41" "420 from circunipolar observations at this station. Pairs 3f sta rb. Adopted seconds of mean N. P. D. //' lU L,atitudc. V " // / // // 6 052 6 082 57 '22 39-45 3 8 44 12 42-49 4-0-51 6 177 6 223 04-82 40-99 2 6 43-05 -0 -05 6 241 6 316 08-99 36-74 2 6 41 -69 + 1 -31 6 395 *6 429 25-72 14 -28 4 7 42-92 +0 -08 *6 429 6 522 14 -28 58 -88 5 7 42-32 +0 -68 6 534 6 583 16-49 17 -41 3 8 42 -15 -0 -85 6 659 6 711 44 -88 12 92 6 12 42-96 ^0 -04 6 734 6 S06 54 74 18 -22 6 12 42-72 -^0 -28 6 763 b 813 42-42 03-10 6 12 43 -62 —0 -62 6 .S24 *6 915 51 -20 37-67 4 7 43 -33 -0 -33 *6 915 6 928 37 -67 52 -Of 6 8 42-73 +0 -27 6 940 7 024 31 '54 19-33 5 II 42 -62 +0 ■3.S 7098 7 126 44-25 36-50 7 13 42 -84 fo -16 7 171 7 253 22-17 49-23 7 13 43 -02 —o -02 7 278 *7 336 50 -85 57 -30 5 7 42-76 +0-24 7 385 7 448 32-98 09 -03 4 10 43 -86 -0 -86 7 512 7 566 03-20 58-74 4 10 43-21 —0 -21 7 595 7 623 06-75 16-38 4 10 43-42 ^0 -42 7 679 7 695 1974 29-9S 2 6 42-41 ^0 -59 7 721 *7 754 21 -09 07 -98 3 6 43-77 -0-77 7 731 *7 754 10-96 07-98 4 7 43-74 -0-74 7 894 *7 983 29-04 34-41 4 7 42 -86 + 0-14 7 9'3 *7 983 13 -08 34-41 4 7 42-45 +0-55 -*6 238 6 3^1 46-34 06 -55 I 3 42-79 +0-21 *6 238 6 318 46 -34 50 -48 I 3 42 -37 Vo -63 6 477 *6 571 52-10 26-74 4 7 42-66 +0-34 6 496 *6 57' 39-21 26-74 4 7 43-41 -0-41 6 687 6 722 30 -87 38 -90 6 12 42 -60 +0-40 6 740 6 867 49 -65 34 -41 6 12 43-13 —0-13 6 926 6 975 33-73 45-95 ■ 3 8 43 -88 -0 -88 6 986 7 076 04 -20 54-08 2 6 43 • 1 1 —0 -I I 7 "48 7 085 29-07 13-97 5 II 43 -05 -0 -05 7 243 *7 336 29-75 57-30 3 6 43-21 —0 -21 7 782 7 843 25-30 24-04 5 II 43-52 —0 -52 *7 855 7 879 or -25 34 -92 3 6 43-15 -0-15 •^7 855 7 88n or -25 12-50 4 7 43-04 —0-04 II idiscriminate mean = 44° 12' 42 " -97. V /eighted mean = 44 i2 43 -00 ±L y -05. e = ±0 " -47. li ["] observations, 36 pairs. [Reduction to A = = +0^-40.] Combination oj 'results. G. W. Dean

. D. // / // // 14-58 3 43 45 34 -88 —0 72 34-00 4 32 -91 ^- 1 25 42 -So 4 34 75 -0-59 20 -60 3 34 3' -0-15 24 56 4 34-47 -0-31 23 -80 5 34-05 -)-o-ii 39 40 3 32 -82 - I -34 10 TO 4 36 -68 -2 52 14 -lo 4 34 46 —0-30 34 -80 4 33-57 -t"0-59 36 -70 4 33-91 +0-25 07 -16 3 33-28 +0 -88 39 '2o 4 34-37 -021 .5" '75 3 33 -04 ^i -12 53 '.so 2 35 ■ ' 5 -0 -99 03 '73 4 33 99 +0-17 55 -31 3 34 78 —0-62 1 1 -.85 5 34 71 -0-55 58 -20 3 33 67 -1-0-49 06-95 4 35 -07 —0 -91 02-57 4 34 -88 -0-72 160 observations, 42 .stars. % = 43° 45' 35"-oi. ^('P„+/ 4672 43-73 8 10 4672 55-44 8 10 39 '25 28 -7,S 7 14 "3 76 52 -24 7 14 40 -5 ' 42-42 7 14 49-11 18 -76 S 14 59 -50 14-64 8 14 06 'lo 54-19 7 14 48 -55 29-95 7 9 48 '55 21 -80 7 9 52 "OO . 22-25 7 9 52 -OO 19-67 7 9 18-51 49-71 7 9 39 '91 49-71 7 9 58-31 13-31 7 14 38 '90 45-46 7 14 00-85 07 -58 3 6 07-58 17-49 4 7 50-44 42-70 8 14 27-70 22 'OO 8 14 14-74 39-71 7 14 08 -63 13-31 6 13 42-56 23-72 8 10 26-59 23 -72 9 10 20 -43 18-35 7 14 27 -38 44-53 6 '3 48-49 49-29 6 13 58-16 38 -07 6 S 38-07 20-67 6 S n -43 33 -02 6 13 57 -28 11-96 7 14 36 -89 40 -oS 8 14 22 -23 09 -68 7 14 11 -21 06 -95 7 14 49-66 35 -97 7 14 59 -45 44 -63 7 9 28 -64 44 -63 7 9 I^alitude. V / // // 3 ' "3 -90 — 0'09 03 -87 — o-o6 03-95 -OT4 04 -21 —0-40 03 -74 -f-o -07 03-62 +0-19 03-70 — Q-II 03-73 -rO-08 03-80 . -^o•oI 04 ■2\ —0-40 04-23 —0 -42 04-09 —0 -28 93 -88 —0-07 04-73 —0 -92 04 -2r —0-40 04-05 —0-24 03-72 —0 -09 03 -84 —0-03 04 -21 —0 -40 03-75 -f -06 03-47 -0-34 04-45 —0 64 04-15 -0-34 04-27 —0-46 04 -01 —0-20 03 -58 -0-23 03 -09 -fo-72 03-92 — o-ii 03-21 —0 '60 04 -48 —0-67 04 -21 —0-40 03 -58 -0-23 03-90 --0 09 04-31 —0-50 03 -oS -0-73 04-04 -0-23 04-51 —070 Indiscriiiiinale mean =43° 31' 03'"-84. Weighted mean =43 31 03 -8iiho"-o5. <»==to"-5o. 333 observations, 47 pairs. [Reduction to A=-f-i"-33-] 276 THE EASTERN OBLIQUE ARC. 15. Agamenticus, Maine. — T. J. Lee. Zenith telescope Military Academj'. First series. Sep- tember 15 to October 10, 1847. One division of level = i^^"28. One turn of micrometer = 44"79i from latitude observations at this station. Pairs 3f stars. 6 5S2 6 662 6 735 6 744 6 75« 6 834 7 377 -■•7 461 7 387 *7 461 *7 533 *7 571 ■"7 533 *7 5«4 *7 533 n 586 *7 542 '•■■7 571 *7 542 *7 584 *7 542 *7 5S6 7 607 7 668 7 693 7 718 7 755 7 798 7 '^29 7 958 *7 997 -<-8 039 *7 997 -■••■8 077 *8 146 *8 039 *S 146 •<-8 077 *8 256 8 188 *S 256 8 268 S 374 *7 4 *7 32 68 164 182 253 395 412 430 Adopted seconds of , mean N. P. D. w Latitude. -. // // / // // 54 '24 47 -oo 3 2 43 13 25 -79 —0 -84 56 -90 28 -90 .5 3 25 -06 ^0 -II 26 63 00 -50 4 3 23 -Si + 1 -14 28 • 1 6 18-13 5 2 26-16 — I -2] 55 ■«4 18-13 5 2 26 -21 -I -26 J 8 '00 19-17 5 25-76 -0-81 18 -oo 10 -37 4 24-03 + 0-92 I 8 'GO 31 -50 5 25 -70 -0-75 25 '30 19-17 4 24 -62 + 0-33 25 '30 10-37 3 23-07 + 1 -88 25 '30 31 -50 4 24-70 +0-25 10 '00 21 -80 5 3 25 -09 —0 -14 36 '97 16-70 5 3 25-24 —0 -29 1970 17-07 6 4 24-88 +0-07 56-32 1 8 ■(:» 6 4 25-56 —0 -61 00 '80 54 -20 5 2 24 -60 +0-35 00 'So 17-60 5 2 24-93 +0 -02 31 74 54 -20 5 2 24-41 +0-54 3>74 1 7 -60 5 2 24-74 +0 -21 08 -48 38 -90 7 3 24-25 +0-70 08-48 00 -32 7 3 24-73 -|-o -22 20 -87 39 -60 2 I 25 -oo - -05 J5-67 39-60 3 2 22 -78 + 2-17 39 -66 33 '26 4 3 25 -oS -0-13 II -90 II -13 4 3 26-18 -I 23 47-50 31 -04 2 2 25-50 -0 -55 15 '52 30 -52 3 2 24-43 +0-52 Luliscriminate mean = 43° 13' 24'' •90. Weighted mean = 43 13 24 -95 =t o'^"io. f = =b o''-99. 121 observations, 27 pairs. [Reduction to A = — o^'-ii.] 15. Aganienticus, Maine.— A. D. Bache, R. H. Fauntleroy, C. O. Boutelle. Zenith sector No. i. Second series. October 4 to November 15, 1S47. Mean value of one division of level =o"'-]2-]. Stars. 7 277 7 39S 7 462 7 731 stars north of zenith. stars. .Adopted seconds of mean. N. P. D. 11' Latitude. t) // / // // 7 091 38 -ID I 43 13 25-78 -0-23 7 171 50-60 5 25 -42 -i-O-13 7 345 51 -60 5 25 -72 -0-17 7 560 24 -60 6 26-55 — I -00 Stars south of zenith. Adopted seconds of mean. N. P. D. «' Latitude. V // / // // 09 -90 5 43 13 25-47 — 0-70 39-75 4 24 -89 - 012 44-90 5 24 26 +0-51 14-50 3 24-45 + 0-32 THE ASTRONOMIC MEASURES. 27; 15. /Ifrainciiticiis, Maine. Second series — continue'l. Stars. Stars nortli Adopted seconds , of mean " N.I'. I). r zenith I.atitnde. 7J stars. stars sonth Adopted seconds , of mean ' N, I'. O. of zenith I.atitnde // / // f f // / // 7 705 41 -17 2 43 '3 24-88 \ -67 7 777 41 -80 2 43 13 24 48 7 S15 1 "06 2 26 -93 .-38 7 H50 34 -«) 3 25-65 7 888 36-40 2 27-46 1 -91 7 972 58 -60 3 24 -89 7 906 15-90 4 25 -04 + "-51 7 994 4 1 ■ 00 1 25-25 8 036 42-56 3 26-34 -0-79 8 136 07 -52 4 24-30 8 107 39 '28 2 23-72 + I-S3 8 345 05 -26 2 24-71 8 224 13 '20 2 25-35 -j-u -20 58 47 -6<-' 3 23-17 8 231 30 -50 4 27 -05 -1 -50 480 43 -20 3 24-96 8 289 40 -30 4 24-21 4 I -34 566 40 -50 3 24 69 16 45 75 3 2371 -f I -84 656 22 -GO 3 25-13 100 07-90 5 25-52 4 -03 821 24 -20 2 25 63 180 39 '2o 2 26-61 — I -06 912 13 -48 2 24 46 330 32 -48 I 24-32 + 1-23 981 26 -90 r 2\ -6S 404 29 -28 2 25 -H6 -0-31 735 03-30 I 25 -06 4 -49 , 19 stars. [Reduction '15 10-25 3 44 'lo 42 'OO 3 02-55 12 71 4 09 '68 42 80 3 38 -88 49 -28 3 oS "60 23 '48 4 16 -GO 35-80 3 22 02 54 -56 3 45 ■''^3 35-14 4 00 -00 49 -50 3 Indiscriminate mean = 42° 58' 59" '37. Weighted mean = 42 58 59 -34 (' = ±0" -67. 115 observations, 30 pairs. [Reduction to A = o" -oo.] 18. Thoiiipsoii, ^Massachusetts. — T. J. Lee. Zenith telescope, Military Acadenn to October 16, 1S46. One division of level =1" -32. observations at this station. Latitude. o / // 42 5« 59 -65 59 -66 59 •71 59-6fj 59 '^> 5'^ '4' 59 '"2 58 -88 60 -36 59 -40 60-13 59 47 59 5 1 60 '60 58 -85 60-68 59-47 59 98 : o" -07. -0-31 — o 32 -0-37 — o -26 — o -46 +093 +0-32 -ro'46 — I "02 — 006 -079 0-13 ~ 017 - I -26 ^049 -I "34 -0-13 — o -64 One turn of micrometer = September 19 45" "064, from I Pairs of stars. -\dopted seconds of mean N. P. D. «' w Latitude. V // // / " ff *6 640 6 690 41 -46 36-72 II 6 42 36 37 -16 -0-S6 *6 640 6 691 41 -46 17-04 5 3 38-16 — 014 6 737 6 810 27-48 37-30 9 S 38-72 —0-70 6 861 -6 966 00-77 30-14 3 2 38-72 —0-70 6 S62 ■*6 966 34-07 .iO- 14 12 7 37 -82 -ro-2o 7 024 -t t 143 50 -20 15-50 14 II 37 -38 +0-64 7 246 7 310 35-" 42-50 14 II 38 -89 -0-87 7 418 7 4S2 04 -So 43-00 13 II 37 99 -fo-03 7 595 7 627 18 -20 50 -20 5 5 37 -97 +005 7 651 7 706 '5-95 1 8 ■ -41 3 6 27-09 ^0-53 6 466 6 516 28-62 35-12 5 7 27 95 -0-33 6 475 6 493 03 '"S 3' -03 4 7 26-66 -96 6 534 6 551 35 '24 51 -12 5 7 27 00 T -62 6 530 6 553 16-57 47-72 5 7 27-96 -0-34 6 655 6 602 45 29 12-25 5 7 26-78 -fO-84 6 659 6 698 50-65 17 -80 5 7 27-23 -0-39 6 718 6 745 17-11 55 -49 5 7 28-14 -0-52 6 740 6 748 45-32 56-32 5 7 27 -oS -0-54 6 771 6 799 38-24 56-31 5 7 27 -86 -0-24 6 827 6 834 41 -92 42-35 5 7 27-75 -0-13 6 847 6 S79 14 -06 31 -87 6 8 28 -iS -0-56 6 862 6 882 03 -06 48 -48 5 7 27-67 -0-05 6 930 6 941 24-48 25-44 5 7 27 23 - 39 6 957 6 976 16-56 12-58 5 7 27-36 +0-26 6 985 6 998 28-51 46-80 6 8 27-15 + 0-47 7 073 7 091 15-92 37 -So 5 7 28-72 — I -10 Indiscriminate mean =42° 14' 27' '-61. Weighted mean =42 14 27 -62zizO'^-o6. C = ±o"-45. 172 observations, 36 p airs. [Reduction to A =+o"-9i.] 284 THE eastb:rn oblique arc. 23. Manomet, Massachusetts. — C. O. Boutelle, F. H. Agnew, and C. S. Peirce. Zenith telescope No. 5. July S to August 2[, 1867. One division of level = o" '951 from observations at this station. One turn of micrometer = \\" '423 from circumpolar observations at this station. Pairs of stars. 4 812 4 S43 4 S73 4 949 4 961 4 974 5 05 s 5 085 5 '«' 5 204 5 336 5 463 5 512 5 525 *5 54 1 5 574 *5 541 5 575 5 62.S 5 702 5 714 5 797 5 847 *5 «7i *5 871 5 •'^SS *5 931 5 950 *5 931 5 951 *5 997 6 062 *5 997 6 06S *6 1S5 6 232 *6 185 6 237 6 341 6 373 6 429 6 470 6 522 6 547 6 57' 6 623 6 637 6 681 6 698 6 734 6 763 •■<-6 784 6 764 -6 784 6 8ro 6 932 6 962 *6 990 6 965 *6 990 7 062 7 103 5 168 5 271 5 295 5 388 5 444 5 459 5 530 5 560 5 602 5 752 5 795 5 863 5 927 5 937 *6 223 6 311 *6 223 6318 tl 631 *6 427 Adopted seconds of mean N. P, D. // // 31 '30 13 -40 15 -GO 14-00 18-20 36-60 52 "26 08 -20 30 -50 45 -00 59 'oo 06 -90 03-00 06 -OO 12 -40 53-60 12 -40 26-80 31 '40 06 -00 23 "37 25-30 02 -80 39-00 39 'oo 47-10 37 '47 26-50 37 -47 08 -70 45 '05 13-54 45 '05 54 -80 07 '85 22 -73 07 '85 05 -41 00-60 44-10 23 "95 21 -[2 54 "08 42-92 r I -30 33 -50 25 -50 25 -60 40 -QO 09-67 56 -38 48-50 23-90 48-50 31 -GO 24-74 07 'OO 43-02 38-12 43-02 24-40 II -48 42 -So 30-00 01 -00 54 -40 57 'OT 18 -40 56-94 50-99 29 "54 55 -80 .6-72 31-01 24-95 56 -80 25-50 37-50 25 -50 20 -80 17-75 03 -82 Latitude V / // // 55 34-56 +079 35-12 +0-23 34 -94 +0-41 35-31 +0-04 35-61 —0 -26 35 -23 -| -12 35 -56 — -21 34-24 + I-II 34 -04 + 1-31 35 -92 -0-57 34-47 +0-88 35-11 +0-24 35-74 -0 -39 35 -82 -0-47 35 -84 -0-49 35-80 •-0-45 35 -48 -0-13 34-83 +0-52 36-53 -1 -18 33-99 + 1-36 35 -75 —0 -40 34-36 +0-99 34-82 +0-53 35 -29 +0-06 34 -Si +0 -54 35-46 — Q-II 35-43 -0-08 35-55 —0-20 36-24 -0-89 36-00 — 0-65 35-06 fO-29 34 90 +0-45 35 -66 -0-31 36-81 -r-46 36-72 - 1 37 34 -80 +0-55 3670 -I '35 35 -87 -0-52 35 -08 +0-27 34-72 +0-63 36-70 -I. '35 THE ASTRONOMIC MEASURES. 285 23. A/anoinci, Massachusetts — continued. Pairs of stars. Adopted stc mean N. OIKlS Ot I'. D. n' w Latitude. V // // / // ff tl 633 *6 427 21 -25 02, -82 6 3 41 55 34 -85 +0-50 6 456 6*520 34-62 08 -00 5 5 35 -82 -0-47 6 530 6 534 50 -92 09-19 5 5 35-91 -0-56 6 5.S2 6 629 53-36 04-14 5 5 34-02 -i-I -33 6 673 X 2 872 09 '04 25-16 6 5 34-63 +0-72 6 714 6 748 39 '9" 13-50 6 5 34-73 +0-62 6 75« 6 867 4071 30 '44 5 5 34-42 -fo-93 6 973 6 976 31-50 18 -20 5 5 35-24 -fo-ii 7 035 7 067 IS -53 25-20 6 5 34-43 +0-92 7 055 7 '52 02 -17 45-62 6 5 35 62 -0-27 7 215 7 246 47-65 57-30 5 5 35-71 -036 7 256 7 28 1 47-80 25-30 6 5 35-43 -0-08 7 306 7 320 56-35 01 -20 6 5 35 -30 -fo-05 5 321 5 341 30-50 48 -69 2 4 35 -60 -0-25 5 535 5 619 52-27 56-15 3 5 34-45 +0-90 5 747 5 853 14-64 54-19 8 5 35-39 —0 -04 5 978 6 106 24-18 04-14 6 5 35-55 — 020 6 23S 6 36cS 27-78 37-64 7 5 35-33 -f 0-02 6 497 6 530 19 -57 50 92 6 5 35-68 -0-33 6 603 6 698 46 -00 40 'OO 6 5 35-43 -0-08 6 745 6 769 15 -20 40 -88 7 5 35-78 -0-43 6 S47 6 940 27 90 16 -70 7 5 35 47 —0-12 6 983 6 997 35-50 53-00 7 5 36-15 — oSo 7 041 7 119 44-76 07 -44 6 5 36 16 — oSi 7 143 7 176 55-00 30 50 7 5 35-59 -024 7 204 7 243 35-44 38 -09 5 5 34 90 -0-45 7 253 7 260 54 -48 06-98 5 5 35-64 — 029 7 277 7 333 36-50 05 30 6 35-66 -0 -31 7 385 7 455 16 -22 38 ■ 1 2 6 35-68 -033 ?5 241 7 5<'5 01 -30 39 -30 35-32 -roo3 7 533 II 4 739 52-74 30 94 33-98 + 1 -37 7 542 7 585 02-52 44-70 36 -52 -1 17 7 623 7 636 39 -55 49 67 35-29 +006 7 696 ■^- 7 706 45-94 12 -22 34-86 +0-49 7 698 *7 706 38 -55 12 -22 35 -32 +0-03 7 754 7 757 ]6 '20 57 -06 5 35 65 —0-30 Indiscriminate mean ^41° 55' 35"-36. ■W^eighted mean =41 55 35 -35 d C = 2rO"-30. 456 observations, 77 pairs. [Reduction to A = o"-oo.] o"-05. tGreenwich, 12-year catalogue. I Groombridge. \ Radcliffe I .-Vrmagh. 286 THE EASTERN OBLIQUE ARC. 24. Sand/ord, New York. — E. Goodfellow. Zenith telescope No. 5. September 11 to Octobers, 1862. One division of level = o"-6'6-]. One turn of micrometer = 4i"'4o. Pairs c )f stars. Adopted seconds of mean N. P. D. n' W Latitude. V // / ' c > / // f/ 6 421 6 468 10 '54 18 -iS 2 4 4 I 27 41 -ID -0-63 6 427 6 470 21 -44 43-64 4 5 40-55 -o-o8 6 475 6 495 03 'I5 17 -94 5 5 39-46 + 1 -QI 6 520 6 556 32 "56 49-71 3 5 40 -35 -f -12 6 530 6 571 16-54 40-61 3 5 41 -46 -0 -99 f 555 6 5 89 45-29 03 -05 3 5 40-50 —0-03 6 629 6 652 36 -40 5' -67 5 5 39-24 + 1 -23 6 698 6 717 17 -87 12-73 5 5 40 -80 -0-33 6 731 6 765 30 '32 20-21 5 5 41 -GO -0-53 6 779 6 806 16 '02 08 -63 5 5 39-74 + 0-73 6 818 6 827 39 77 41 -23 5 5 39 -84 +0-63 6 861 6 866 2970 20 -41 5 5 40-28 +0-19 6 867 6 882 18-43 48-14 5 5 40-50 -0-03 6 937 6 962 52-17 00-85 5 5 41 -08 — o-6i 6 965 6 967 31 '46 51 -70 5 5 40-78 -0-31 6 970 6 975 19 '59 18 -96 5 5 40-78 -0-31 7 027 7 041 48 -64 42-55 5 5 40 -11 +0-36 7 013 7 060 30 '34 01 -41 5 5 40 -61 — 0-14 7 0S4 7 112 38-26 42-64 5 5 40-21 +0-26 7 120 7 164 14 -32 53 -66 5 5 41-52 -I -05 7 153 7 194 28-30 56 -08 5 5 40-52 —0-05 7 182 7 204 15-88 41 -47 3 5 39-08 + 1 -39 7 19S 7 213 10-26 51 -72 3 5 40-30 +0-17 7 220 / 275 46 -93 19 -00 5 5 40-99 -0-52 7 297 7 333 II -23 16 -lo 5 5 40-47 -00 7 345 7 373 17-46 04 -ID 5 5 41 -09 —0-62 7 365 7 368 57-34 14 -60 5 5 39-u + 1-36 7 3«7 7 410 15-27 24-12 5 5 39-87 +0 -60 7 418 7 449 02 -07 53 -50 5 5 41 -42 -0-95 7 455 7 462 55 '34 53 -56 5 5 39-58 -1-0-89 7 474 7 495 50-94 54-45 5 5 40-38 +0 -09 7 503 7 505 00 -96 58-97 5 5 40-79 —0-32 7 544 7 554 04 "43 II -92 5 5 40-38 +0-09 7 571 7 5S2 13-99 06 -68 5 5 41 -30 -0 -83 7 585 7 595 07 -30 54-97 5 5 41 -39 —0 -92 Inc We 161 liscriminate mean =41^ ighted mean = 41 observation.s, 35 pains. [Reduction to A = 27' 40'' 27 40 ''-39. - o"-39 •47- -47 ±0 •] '' -08. THE ASTRONOMIC MEASURES. 287 25. M'^es/ Hills, New division of level = o"i6 circiuiipolar observations York.— A. T. Mosinan. Zenith telescope Xo. 5. Auj(ust 8 to 24, 1865. One from observations at this station. One turn of micrometer = 4 1 "397 from at this station. I Pairs of star.s. Ado])ted secoiid.s of mean N. P. D. n' w Latitude. V // // / // // 5 617 5 644 08 '60 07-17 6 16 40 48 50 -85 -0-79 5 643 5 677 34-15 52 -20 4 14 49-69 +0-37 5 65J9 20-97 4 14 49 67 +0-39 5 714 5 801 1 2 '37 33 -63 6 16 49 5' -f-o-55 5 752 5 798 44-57 42-17 4 14 49-66 +0-40 5 «4o 5 856 17 'OO 03 -62 6 16 49 -69 +0-37 5 842 5 9'i 08 -18 30-90 6 16 50-14 —0 -08 5 874 5 944 26 -89 33 •■•S 7 16 49-97 +0-09 5 922 5 95'> 06-55 21 -74 6 16 49 69 +0-37 5 97S 6 030 16 -50 57-54 4 14 49-99 +0-07 6 005 6 079 39-91 18-50 5 15 50-27 —0-21 6 013 6 082 18 -60 46-33 4 14 50-14 —0-08 6 147 6 246 19 -20 36-34 6 16 50 -86 — 080 6 231 *6 311 34-70 43-54 6 10 50-33 -0-27 6 251 *6 3 1 1 '9-5« 43-54 7 II 49-91 +0-15 6 373 6 43« 50 -58 06*00 6 16 49-76 +0-30 6 3«7 6 410 49 -80 40-32 6 16 49 -53 +0-53 6 421 6 427 59-06 09 -70 6 16 50-17 — o-ii 6 468 6 516 04-95 20-19 16 50-06 0-00 6 473 6 493 06-94 16 -96 6 16 49 -75 +0-31 6 534 6 566 1974 08 -09 5 15 50-22 — 016 6 553 6 579 32-65 49 -90 6 16 49-52 -ro-54 6 581 6 656 04 -86 24-97 6 16 50-21 -0-15 6635 6 690 26-65 17 -90 6 16 50 -40 -0 -34 6 698 6 721 57 -50 42 -01 6 16 50-07 — 001 6 711 -6 728 49-64 40 -82 7 II 49-94 +0-12 *6 7 28 6 765 40 -82 53-"S 6 10 50 50 -0-44 6 74S 6 762 30 -36 07-17 5 15 49^83 +0-23 6 Sio *6 81 8 50 -75 12-44 6 10 49-99 +007 *6 818 6 866 12-44 51 -90 6 10 49-33 +0-73 6 827 6 863 14-45 19-10 6 16 50-93 -0 -87 6 868 6 905 00 -27 24 -45 6 16 50 -37 —0-31 6 S76 6 937 40-77 23 -10 6 16 50-15 — -09 6 915 6 965 52 -4S 00-62 7 16 50 -^^ —0 03 6 966 6 976 04-42 40-94 6 16 49 -87 +0-19 6983 6 998 56-65 15-02 6 16 50-15 — 009 7 022 7 041 25-46 07 -86 7 16 50 -47 -0-41 7 064 7 117 19-71 01 -71 7 16 50 -21 -0-15 Im iscriminate nean = 40° 48' 50" -06. Wl iijhted mean ,: 40 48 50 =to" -34. ■06 rb 0" -04. 223 observations, 39 pairs. [RodiK-tion to Js,= — o"-i6.] 288 THE EASTERN OBUOUE ARC. 26. Ne'iS.' York, New York. — E. Goodfellow. Zenith telescope No. 5. June 22 to 25, 1S5S. (_)ne division of level = o"'845. Pairs of stars. One turn of micrometer = i\\"'^i6. .\ilopted .seconds of mean N. P. D. I.atitude. 4 640 ■4 S04 4 845 4 885 *4 952 *4 952 5 113 5 244 5 336 5 385 5 448 .'S 599 *5 752 *5 752 *5 902 *5 902 6 005 *6 079 6 251 6 387 6 476 6 534 6 64S 6 697 4 726 4 SoS 4 S64 4 897 5 000 5 036 5 204 5 313 *5 400 *5 400 5 502 5 677 5 798 5 860 5 9*57 5 988 -6 079 6 223 6 31S 6 410 6 491 6 579 6 687 6 740 05 '82 41 '06 3 05 -42 1 1 -96 3 41 -90 57 76 4 13 -08 06 -54 4 35 -82 49 77 4 35 "82 1 1 -25 4 50-58 01 -05 4 39 •10 51 •66 4 27 -68 58 -95 4 45 '50 58 -95 4 14-58 14-87 4 20-95 08-13 4 06 -46 ( )9 -57 4 06 -46 23-12 4 29 -36 09 -8 1 4 29-36 48-41 4 27 -06 13 "So 4 13 '80 36-38 2 29-16 41 -44 3 II -34 06 -13 3 59 '38 09 -58 4 55 '92 25 -75 4 13-28 .12-72 4 16 -61 17 '46 4 Indiscriminate mean = 40° 43' 4.S' Weighted mean = 40 43 48 '■= -to" -45. 90 observations, 24 pairs. 4 4 5 5 3 5 5 3 3 5 5 3 ,3 3 3 3 3 4 4 5 5 5 5 ■43- ■39 =* 40 43 47 72 47-72 47 '28 48 -06 48-86 47-36 49-10 47-53 4S-86 49 -63 48 -24 48 -14 48 -50 47 -5« 4''-i -95 48-62 48 -95 48 -82 49 -58 49-17 49-13 48 -06 48-51 48 -02 /'•09. ^o -67 r'5 '67 t- 1 - 1 [ +0-33 -o -47 -^i -03 — o -71 ho -86 -o -47 -1 -24 +0-15 -fo-25 — o -II ^o-Si -o -56 -0-23 - o -56 -'• -43 -1 -19 — o -78 -o -74 -T-O -33 — O "12 +0-37 [Reduction to center of transit <>r A = +o''-2i.] riUi ASTRONOMIC MKAvSURKS. 289 27. I'icacon Hill New Jcrscj . — J. P.. liaylor. Zciiitli Ic-k-scope No. 4. July 24 to Auj^usl 27, 1875. One division of level =2"u4. One turn of niiironieler =43"'462 from circunipolar observations at l.his station. I'airs of .star.s. * 5 400 5 432 \S 463 5 523 5 629 5 703 *5 Soi *5 Soi 5 931 5 997 *6 082 6 193 *6 232 *6 232 6 300 6 357 6 43S 6 476 6 530 6 571 6 602 6 697 6 7 28 6 Soo 6 S62 5 596 5 951 6 084 6 1 84 6 23S 6 71 1 6 745 6 810 5 411 *5 463 5 479 5 546 5 677 5 7S5 5 828 5 860 5 937 *6 0S2 6 095 6 203 6 246 6 258 6 34S 6 404 6 463 6 497 6 547 6 579 6 68 1 6 714 6 771 6 S30 6 933 5 604 6 "33 6 09 r 6 223 6 335 6 718 6 765 6 867 Adopted seconds of mean N. \'. D. 3 5 7 5 5 6 7 6 7 6 7 7 7 7 7 6 6 7 6 7 7 6 7 6 6 3 5 5 5 5 6 5 5 =40° 22' 27"-84. =40 22 27 •Sid=o"-o7. (■=rbo"'42. 195 observations, 33 pairs. [Reduction to iA=o"'oo.] 46 •s.s ^ -( K ) 23 74 17 '20 17 -20 20 -84 29 -40 "4-37 47-64 56 -oo 58 75 53 -32 22-52 43 -46 22-52 29 -70 01 -51 19 -66 01 -30 53 -10 53 ■!» 16 -61 37 '14 56 -45 1 2 -63 21 -59 12 -63 31 -66 55-06 58 -33 29 -60 29 -83 25 '60 50 -95 45-92 41 -16 10-05 01 -35 25 -20 41 -80 52 -77 28 -68 09 -04 40-44 22-43 47 -42 28 -50 24-52 (X) -07 17-42 35 -60 10 -20 29 -So ol -85 15-09 44-68 40 -87 16-26 16 -So 40-07 32 -99 36 -89 09-51 30 -62 22 -04 14-83 7V latitude. V / // // 6 40 22 27 -73 -0 -08 4 28-95 I -14 5 27-77 : -04 7 26-86 •-0 -95 7 26-78 1 -03 7 27-58 ro-23 5 27-59 4-0-22 5 28 -6<) -0-79 7 28 -15 '> -54 5 28 -02 - f) -21 5 28 -64 -0-S3 7 26-95 -0 -86 5 28 -08 —0 -27 5 27-65 ~o-j6 7 28 -30 -0 -49 7 27 -3(j -0-51 7 28-31 0-50 7 27 -62 0-19 7 27-66 • o-iS 7 27-41 -0 -40 7 27 -38 - -43 7 27-10 -0-71 7 27-50 •0-31 7 27 -61 +0-20 7 27-46 -0-35 6 27 -39 -;-o -42 i 28 -24 -0-43 7 28 -I I —0 -30 7 27 -87 — -06 7 28-26 -045 7 28 -26 -045 7 28 -67 -0-S6 7 28 -97 -I -16 Indiscriminate mean Weighted mean 4192 — No. ■19 290 THE EASTERN OBLIQUE ARC. 2S. Mount Rose, New Jersey. — J. E. Hilganl. Zenith telescope Nt). 2. July 19 to August 3, 1S52 One division of level =i''''"oo, from observations at this station, (^ne turn of nncronieter=44"75o, from circunipolar observations at this station. Pairs of stars. t2 2S5 5 302 5 33S 5 432 T 211 5 383 1 276 5 38-' 5 463 5 479 5 4S9 1 448 5 62S 5 686 5 674 5 74f 5 702 5 728 5 7S5 5 922 5 '^2' 5 S23 5 941 5 972 5 967 ii 539 6 178 6 255 6 216 6 223 6 322 % 348 6 341 *6 348 6 460 6 563 6 487 6 586 6 5«5 6 625 6 623 6 690 6 648 6 697 6 735 6 749 *6 817 *6 817 adopted mean seconds of N. P. D. // >' 52 -45 25-61 00-55 48-80 13 -So 40 -84 3' '3' 17 -60 54 75 58 -92 57 '60 GO -94 47-42 40-14 24-66 19 '65 35-40 50-42 59 "46 26 -36 14 -rxi 10 -50 41 -66 16-26 54-96 43 'lo 42 •6r 04 • 1 2 39 73 43 "30 24 -26 58 -45 39 '2 1 58 -45 05 '74 49-76 44-76 08 -27 19 -So 20 -26 10 -44 52 -60 53 77 01 -73 26-44 06 -40 27-66 27-66 IV IvStitjuie. T / / ' // 4 40 22 05 -GO + 0-41 6 05 -54 — 0-07 4 05 -26 + 0-15 4 04 -62 + -79 6 05-75 -0-34 6 05 -60 — -19 4 05-65 -0-24 6 04 -66 + -75 4 05-89 — 0-48 6 04 -83 + -58 4 04-56 + 0-85 6 05 -48 — 0-07 4 05-14 -f-o -27 4 g6 -62 — 1 -21 4 05-52 ^G-II 4 05 -00 +0-41 3 05 -23 +0-18 4 05 -84 -0 -43 4 05 -29 +0 -12 4 06 -29 ~o -88 6 04 '93 +0 -48 4 06 -33 — -92 4 06 -70 -[ -29 6 04 -84 +0-57 Indi.scriminate mean =40° 22' o5'"-44. Weighted mean =40 22 05 -4i±o' ,. =±o"-82. 81 observations, 24 pairs. [Reduction to A =o"-oo.] ■oS. t Groouil^ridge. J Greenwich 12 year Cat. 1845. THK ASTRONOMIC MP:ASrRHS. 291 29. )'ard, Pennsylv;iiii;i 1854. One division of level at this station. — J. H. Hilj(anl. Zenith telescope No. =f)"'.S<), One tnrn of niicronieter=76''''i 6. October 17 to November 2, 5, from circiimpolar obsevations I'airs nl' stars. I I I 7 "29 7 085 *7 (.91 7 "31 *7 091 7 132 7 141 7 144 7 1.S2 7 194 7 213 7 253 7 260 "7 297 7 277 "•■■7 297 7 3'3 7 326 7 363 7 372 *7 399 7 469 *7 399 7 480 7 402 7 462 7 521 7 554 7 560 7 607 7 610 7 674 7 696 *7 712 7 69S -7 712 7 727 7 731 7 757 7 787 7 805 7 851 7 878 7 90>'^ 7 937 7 973 7 984 8 037 8 059 8 156 8 082 *8 159 8 114 *8 159 8 177 8 .87 8 206 8 231 S 279 S 299 8 312 8 3 '4 8 355 26 32 46 60 67 80 87 114 156 i66 180 Adopted seconds of mean N. I'. U. "' ^l> l.atiUiiU. 7' f f // / // // 43 '69 '3-97 6 13 39 58 28 -58 4-0 -81 14 '03 06 -40 4 6 29-63 — 024 14 '03 02-45 4 6 29-98 -0 59 29 "97 (;9 -66 3 6 2916 fo-23 58 -3 > 39-23 8 17 29-63 —0 -24 38-34 49-23 4 9 29 -60 — 0-2f 02 '53 01 -90 4 6 29-46 — -07 34-06 01 -90 6 9 30-04 -0-65 5378 4971 I 2 29 •90 -0-51 II -25 56-30 4 9 ■ 28 -54 + 0-85 50-15 02-33 1 1 29-40 — o-oi 50-15 05 -90 6 9 29 54 -0-15 59 78 57 -oi 5 II 29-66 -0-27 24-76 21 -7,S 4 9 29-36 +0-03 30-78 13-72 5 II 28-64 +0-75 31-90 00 -40 4 9 29 39 0-0() 31 -90 21 '34 4 6 29-53 — 0-14 24-82 21 -34 4 6 28 -83 +0-56 46 -90 10-96 4 9 28-36 -ri 03 51 -26 27-72 6 '3 30-54 -1 -'5 26-30 45-57 6 13 29 20 +019 45 '53 46 02 2 4 29-08 +0-31 05-55 44-06 5 1 1 29-72 -0-33 01 -43 43-56 2 4 30 57 -I -iS 56-11 •5-'7 5 1 1 30 -30 —0-91 26 •!() 59-20 2 3 29 29 -f-o-io 54 -80 59-20 5 7 29-51 — 0-12 20-32 43 -'3 5 1 1 29 40 — -0 1 48-41 u -18 4 9 28-78 +o-6i 47-96 23-42 5 1 1 29-57 — u'lS 27 -22 07 -98 2 4 29 -Si — 0-42 50 -42 41 42 3 6 29 35 -roo4 19-17 41 -97 3 6 29-17 +0-22 II -90 23 95 3 6 30-08 —0-69 25-14 08 -70 3 6 28-75 +0-64 14-77 •8-54 3 6 28 -30 + 1 09 19-38 20 -5 1 4 9 29-31 +0-0S Indi.scriniinat e mean =39° 58' 29" -41. Weivjhted nie ui =39 58 29 ■39^0 " -06. <=±o" -68 148 observations, 37 pairs. [Rednction to .\ =0" -on.] Ik ' 292 THE EASTERN OBUOUE ARC. For the abstracts of results corresponding to the astronomic latitudes of the fol- lowing stations, numbered from 30 to 53, inclusive, that is, for stations common to the transcontinental arc and the oblique arc, see ' ' The Transcontinental Triangulation ' ' United States Coast and Geodetic Survey Special Publication No. 4; Washington, D. C, 1900. The final sunmiary of the results for latitude includes the adopted latitude at these stations: D. C. 30. Principio, Md. 31. Maryland Heights, Md 32. Pooles Island, Md. 33. Sugar Loaf, Md. 34. Dover, Del. 35. Webb, Md. 36. Soper, Md. 37. Rockville, Md. 38. Taylor, Md. 39. Strasburg, Va. 40. Cape May, N. J. 41. Caiisten, D. C. 42. Naval Observatory (new) 43. Hill, Md. 44. Naval Observatory (old), D. C. 45. vSeaton, D. C. 46. Coast and Geodetic Snrvej' Office, D. C. 47. Bull Run, Va. 4S. Marriott, Md. 49. Cape Henlopen, Del. 50. Clark, Va. 51. Elliott Knob, Va. 52. Charlottesville, Va. 53. Long Mountain, Va. 54. y)/06>r^. North Carolina. — J.B.Baylor. Zenith telescope No. 2. First series. November 8 to December 6, 1876. One division of level=i' polar observations at this station. '■06. One turn of micronieter=44'''"S57 from circunu Pairs of Stars, 7 943 7 973 8 068 8 071 8 107 8 146 8 171 8 206 8 245 8 256 7 26 100 109 130 153 219 264 318 349 388 438 456 476 518 568 595 615 656 661 740 79' 796 S27 863 903 9^5 953 981 1 017 1 030 1 057 I OQQ J 126 Adopted mean seconds of N. P. D. 11' 7V // // 44 '53 43-67 7 3 54-41 58-9' 6 3 18 72 01 '91 6 3 12 -67 32. 56 7 3 42 TO 29-75 5 2 02 79 21 -38 9 3 28-90 55 -78 7 3 19 '20 08 -34 6 3 32-13 oS -30 7 3 08 '41 09-42 6 3 19 '60 28-61 6 3 rg -26 2i -30 6 3 26 -68 31 -CO 7 3 45-44 48-21 8 3 0044 47-9' 6 3 23 -64 07-52 4 2 34 -62 52-24 5 2 '4 -63 20 -50 7 3 57 -00 28-81 7 3 39 -36 01 -35 6 3 37 -46 31 -60 7 3 19-53 24 -60 6 3 Latitude. 36 23 55-62 -0 -54 55 -67 -0-59 53 -85 + 1 -23 54-87 4-0 -21 54-88 '|-o -20 54-29 +0-79 55 -65 -0-57 55-84 -0 -76 54-63 +0-45 55-27 —0 -19 56 ■■6 — J -08 55 -18 —0 -lo 54 -89 +0-19 55 -16 -0 -08 54-99 -1-0 -09 56-87 - 1 -79 55 -89 -o-8i 56 -73 i-65 53 -/o ^-1-38 53 -59 -1- 1 -49 53 -84 l-i -24 54-97 +0 -II Indiscriminate niean=36° 23' 55"-i2. Weighted mean =36 23 55 -o8±o''"i3. ,.= ±i''-o6. 140 observations, 22 pairs. [Reduction to /i:,= — o"-o4.] THE ASTRONOMIC MEASURES. 293 I 54. Afoore, North Carolina. — W. B. Fairfield. Zenith telescope No. 2. Second series. Novem- ber 23 to December 6, 1876. One division of level = i''()6. One turn of mi. D. u' // // 44 -53 43-67 6 54-41 58 -9 r 6 1872 01 -91 5 12-67 32 -56 6 42 •!() 29-75 6 0279 21 -38 6 28 -90 55 -78 6 19 20 08 "34 6 32-13 08 -30 6 08-41 09-42 6 19 '60 28 -6 r 6 19 26 23-30 7 26-68 31 -oo 7 45-44 48-21 6 00 "44 47-91 5 23-64 07-52 6 ■4-63 20-50 6 57-00 28-81 6 39-36 01 -35 6 37-46 31 -60 6 19 -53 24-60 6 w Latitude. V / // // 3 36 23 56-04 — I -22 3 55-14 -032 3 53 95 + -87 3 55-13 -0-31 3 54 -87 — 05 3 53 -82 + 1 "OO 3 55 -55 -073 3 55-41 -0-59 3 52 76 +2-06 3 55-4' -0-59 3 54 -86 —0-04 3 55 -69 -0 -87 3 53 -58 +1 -24 3 54-50 +0-32 3 55 -21 -0-39 3 56-47 -1-65 3 54-90 — 008 3 54-03 -fo-79 3 55 37 -0-55 3 53-76 + 1 -06 3 54-74 +o-o8 Indiscriminate mean =36° 23' 54"-S2. Weighted mean =36 23 54 •82±o"-i3. c=±o"-e~. 126 observations, 21 pairs. [Reduction to A, = — o''''-o4.] adopted value =36° 23' 54'"-95d=o"-09. [Reduction 10^;^ = — o"-o4.] 294 THE EASTERN OBLIQUE ARC. 55. Yohug, North Carolina. — H. W. Blair. Zenith telescope No. 4. First series. October 14 to 21, 1876. One division of level = 2"'2o. One turn of :nicronieter=43"'388 from circuinpolar observations at this station. Fairs of stars. Adopted seconds of mean N. P. D. n' "£/ Latitude. V // // / // // 6 S56 6 S58 21 -95 36 -45 6 2 35 44 22 -88 - 1 -35 6 962 6 966 3T '57 oSt5 5 2 22 -90 -1 -37 7 022 7 029 20 -95 32-26 6 2 2 1 -63 — Q-IO 7 174 7 194 35 '03 55 '55 6 2 20 -68 -0-85 7 253 7 256 53 -oS 46-94 6 2 20 -27 -l-I -26 7 399 [■ 909] 21 '60 45 --S I 6 2 23 -20 -1-67 7 465 7 521 59 'og 33 74 6 2 22-88 -I -35 7 5S5 7 59S 20 •17 49-61 6 2 20-50 t I -03 7 712 7 746 GO • 1 2 20 -3 1 6 2 20 -36 ^I -17 7 914 7 972 20 -45 46-74 6 2 21 -36 -; 0-17 8 082 8 160 15 -54 41 -38 5 2 20 -84 -1 -69 8 114 8 131 43 -23 17-15 5 2 2ig. North Caroli 12 to 20, 1876. One division tions at this station. na. — J. B. Boutelle. Zenith telescope No. 5. Second series. December of level=o"'98. One turn of micronieter=4i"'56i from latitude ohserva- Pairs of stars. AQoptea mean seconas 01 N. P. D. //' W Latitude. V // // / " // 8 256 t4 172 2975 54 '74 5 4 35 12 13 -39 —0-02 8 364 8 370 30-10 37-17 5 4 13-24 +0-13 26 92 21 -38 43-09 5 4 14-25 —0 -88 lOI 153 37-13 08-34 5 4 14 -22 -0 -85 178 189 03 -04 13 -57 5 4 14-34 -0-97 198 264 40-18 08-30 5 4 13-62 -0-25 283 349 1 8 -68 09-42 5 4 14-08 -0-71 515 561 31 -11 18 -20 5 4 12-39 +0-98 569 628 34 -25 58 -85 5 4 12-43 +0-94 682 735 21 -44 03-14 5 4 12-58 +0-79 769 7S5 46-25 56-30 5 4 12 -69 +0-6S 842 863 51 -60 14-63 5 4 13 -32 +0-05 904 912 59 '45 05-47 5 4 13-62 -0 -25 947 966 51 -12 59-89 5 4 12 -20 4-1 -17 983 I 025 37-96 09-77 5 4 14-40 -I -03 I 069 I 099 29-64 19-53 5 4 12 -70 +0 -67 I 123 ! 132 17-54 03-57 5 4 14-30 -0 -93 I 155 I 210 32-ri 41 -87 5 4 13-26 +0 -I I I 289 I 287 25 -64 29-74 5 4 13-05 +0 -32 1 301 I 311 42 -80 43-20 5 4 13-40 -0-03 Indiscriminate mean = = 35° 12' 13" -37- Weighted mean = e = ■35 ±0 12 13 "•34. •37±o" II. 100 observations, 20 pairs [Reduction to A = + i6''-o7.J Adopted value = 35° 12' 13" ■3i±o" 07. [Reduction to A = =+i6"-o7.] t Groombridge. THE ASTRONOMIC MEASURES. 297 57. Paris, .South Carolina. — J. B. Boutelle. Zenith telescope Xo. 5 I7> •'^VS- One division of level=o""944. One turn of niicronu'ler=4i"5 at this station. First series. October 4 to 14 from latitu'le observations Fairs of .stars. 6 810 6 876 6 941 7 029 *7 103 7 152 7 200 7 271 7 44« 7 512 7 554 7 664 7 731 7 798 7 888 7 914 7 972 8 052 8 182 8 206 8 227 8 2S0 6 830 6 882 7 007 7 061 ■■•7' 103 7 '5S" 7 262 7 377 7 450 7 520 7 607 7 683 7 777 7 «5o 7 900 7 932 8 032 8 056 8 1 88 ■ 8 212 8 252 8 3CX5 Adopted seconds of mean N. P. D. n' 7V Latitude. T // // / // // 22 '04 24-52 5 5 34 56 3' -6" + 046 04-16 42-50 6 5 33 -'3 -I -07 08 -57 35 -26 6 5 32-61 -0-55 43 72 10 -03 5 5 33-00 -0-94 35 32 35 -32 5 3 31 -44 + 0-62 10 -61 41 -85 5 5 3' -08 + 0-98 29 '45 45 '40 5 5 31 -'o + 0-96 31 -86 37-85 5 5 30-63 + 1 -43 47 "08 53-92 5 5 32 30 — 0-24 29-36 33-53 5 5 31 93 +0-I3 42 -05 24-88 5 5 32 44 -0-38 40-76 07-67 5 5 32-38 -0-32 04-25 22 -80 5 5 33-06 — I 00 54 74 00-34 6 5 32-21 -0-15 58-00 09 -09 5 5 32 -73 —0 -67 40-15 10-15 6 5 32-33 -0-27 05 77 41 -03 5 5 31-57 -fo-49 22 -06 26-86 5 5 3' -71 +0-35 43 65 23 -73 6 5 31 -90 +o-i6 52 -60 08-68 6 5 32-18 —0-12 29-70 26-95 5 5 31 -90 +0-16 57 77 53 -55 5 5 31 -77 4-0 29 Indiscriminate mean =34° 56' 32^-05. Weighted mean =34 56 32 -o6rto'''-io. c=±o"-T,6. 116 observations, 22 pairs. [Reduction to A, = — o''''-87.] . 298 THE EASTERN OBLIQUE ARC. 57. Paris, South Carolina. — H. W. Blair. Zenith telescope No. 5. Second series. October iS to 25. '875. One division of level = o" 944. One turn of micrometer = 41" -386 from circnmpolar observations at this station. Pairs of stars. 7 204 7 260 7 437 7 495 7 606 7 674 7 7:vS 7 807 7 871 S 003 S 028 8 099 8 261 8 345 82 ]02 189 226 *334 339 416 470 7 213 j-2 065 7 455 7 553 7 64? 7 696 7 796 7 855 7 912 8 or3 8 097 s 171 8 324 4 92 I 21 215 250 *334 370 454 508 idopted seconds of mean N. P. D. // // 49-16 •13 -74 19-40 53-66 41 -or 34-65 28 -93 4: -30 40 -50 32 -40 59 'PS 27 -52 37 -82 26 -07 58-19 35 -56 17-85 07-72 19-56 16-54 5" -74 58 -93 14 -18 32-48 25 "03 1 1 09 43 '34 58-21 37-80 03-14 25-44 05 -15 33-37 47-45 01 -QI 55 -02 33 -49 33 '49 56-08 44-07 55 -oo 21 -54 54 -50 18 -61 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Indiscriminate mean = 34° 56' 3 Weighted mean =34 56 3 e = ± o"-27. no observations, 22 pairs. [Reduction to A = -o."87.] Adopted value =34° 56^31 [Reduction to A = — o-''87.] w I,atilude. V / // '/ 6 34 56 31 -57 +0-29 6 32 -02 —0 -16 6 32 -68 ~o -82 6 31 -30 +0-56 6 31 -56 +0-30 6 31 -72 ^-o -14 6 3' -70 +0-16 6 30 -88 +0-98 6 31 -32 +0-54 6 32-21 -0-35 6 3' -57 -I-0-29 6 32-54 -0-68 6 32 -06 —0 -20 6 32 -06 — 0-20 6 .^2 -39 -0 -53 6 31 -92 — -06 6 32 -03 -0-17 6 32-71 -0-85 3 33 -33 -1-47 6 30-99 +0-87 6 30 -90 +0-96 6 32-13 —0 -27 i" ■88. I -86 rfc 0" -oS. -96 ±o"'07. tKadcliffe Catalogue. THE ASTRONOMIC MKASIRKS. 299 58. Currahcc, Georgia. H. \V. Blair. /Aiiith tck-sc(jpe Xo. 5. I'irst series. September 2S to October 8, 1874. One division of level = o"'94 from observations at this station, (^ne turn of micrometer = 4i'''''38i from circumpolar ob.servations at this station. I'air.s f .stars. 6 571 6 599 6 637 6 656 6 697 6 739 6 764 6 794 6 824 6 839 6 858 6 895 6 944 6 963 *6 998 *6 998 7 008 7 067 7 094 7 105 7 215 7 257 7 275 7 301 7 350 7 377 7 402 7 444 7 474 7 480 7 528 7 548 7 606 7 612 7 641 7 683 7 705 7 706 7 807 7 820 7 855 7 856 7 9'5 7 923 7 953 8 003 8 023 8 032 8 076 8 079 8 097 8 128 S 158 8 182 8 250 8 280 Adopted mean seconds of N. I'. D. h' w I,;ititiule. V // // / // // 31 74 22 -34 5 5 34 31 37-32 -i-o-43 40 -03 22-44 5 5 38 -05 —0-30 "6 54 26 -40 5 5 38-32 -0-57 26-47 20-20 5 5 37-73 +0-02 51 -47 49 -75 5 5 37-53 4-0-22 54 76 42 24 5 37-60 + 0-15 45-15 08 -25 6 37 -64 +0-1 1 35-87 35 -87 5 38 -33 -0-58 35 -'7 02 -5 1 5 38 -03 -0-28 10 -28 49 94 5 38 -46 -0-71 18 '44 40-94 5 38 -50 -0-75 35 -60 12-52 5 38-09 -0-34 29-42 52-53 5 36-15 -1 -60 00 -J,}, 01 -55 5 36-19 -■•56 43-96 51-78 5 38-29 -054 oS-14 17-84 5 36-64 -pi -11 57-'2 25-68 5 37-30 +0-45 13 -87 24-94 5 38 - 1 2 -0-37 54-13 10-13 5 36-97 +0-78 16-25 43-26 5 37-22 +0-53 53 -84 06-71 5 38 -05 -0-30 56 -37 13 -32 5 37-81 — o-o6 51 -15 38-76 5 38-41 -0-66 01 -48 00 -52 5 38-59 — 0-S4 55 -39 57 -83 5 38 -55 — o-So 18-56 40 -85 5 38 -29 -'> 54 21 79 03 -5" 5 37 -36 * -39 03 -95 17-82 5 37 60 +o-'5 scriminate mean = 34° 3>' 37" -75- ^hte^7 7 437 7 561 7 565 7 623 7 674 7 71S 7 749 7 796 7 .S25 7 900 7 912 7 961 8 052 8 no 8 136 8 159 8 299 8 307 7 14 dopted mean second.s of N. 1'. D. ;/' IV Latitude. V // " / // // 22 -53 51 -94 5 3 34 31 37 -06 +0-65 31 "94 21 -70 5 3 37-31 +0-40 09-44 32 •21 5 3 37 -87 —0 '16 00-45 14 -00 5 3 36-94 +0-77 13 '63 08 -54 5 3 37 -62 Ho -09 08-66 18 -50 5 3 37-70 +0-01 56 '30 15 '3' 5 3 37 -53 +o-i8 I 2 -59 42-42 6 3 36-88 +0-83 16-28 25-96 5 3 37-90 —0 '19 10 -35 44 -[2 6 3 37 -72 —0 -01 18-79 26-68 5 3 36 -93 +0-78 26 -43 55-62 5 3 37-19 +0-52 41 '45 15 -02 5 3 39-61 — I -90 iS -26 24-47 5 3 38 -77 — I -06 45 '87 43 -29 5 3 39 -37 -I -66 42-54 20-15 5 3 37-00 +0-71 Indiscriminate mean = 34° 31' yi"'1\. -Weighted mean =34 3^ 37 -71 f = =b o"-49. 82 observations, 16 pairs. [Reduction to A = + 6"-2i.] Adopted value =34° 31' 37''-75 [Reduction to A = ^b"-2\.'\ ± o"-i4. :o"-oS. t Armagh, 1840. 'I thp: astronomic measures. 301 59. Lavender, Georgia. — F. P. Webber. Zenith telescope No. 3. October 20 to November 4, 1874. One division of levels i^^'20. tions at this station. One turn of niiiTonieter=46'''''6a deterniint I'airsof star.s. Adopted mean seconds of N. P. I). h' 7V // // 7 310 7 350 1279 29-42 8 3 7 553 7 582 57 -49 49-75 6 3 7 607 7 614 41 -5' 09 -32 5 3 7 643 7 664 07 • 1 2 56 •90 5 3 7 712 7 729 34 '99 56-79 6 3 7 S20 7 856 43 '26 06 -71 7 3 7 ''^79 7 923 29 '57 13 -32 5 3 7 997 8 059 22-27 25 -08 6 3 8 097 8 118 17-90 50 -3" 5 3 8 r49 8 '5S 33 -Si 21 -79 5 3 8 2S2 8 300 12-56 13-53 5 3 79 lOI 42-48 17-29 5 3 121 156 25-11 40-70 5 3 180 214 44-91 36-50 5 3 305 339 55-35 15-39 5 3 377 395 30-80 55-68 S 3 560 572 5273 20 -70 6 3 587 644 13-00 II -68 5 3 7 559 7 568 50 -89 32-05 5 -« 7 641 7 668 13-87 39 22 5 3 7 855 7 900 53-84 26 -68 5 3 7 962 8 032 47-41 00-52 6 3 S 058 8 131 34-35 56-50 5 3 8 160 8 224 • 21 -00 27-85 7 3 142 169 16-58 14 -So 5 3 219 247 1 r -45 40-63 5 3 321 343 38 -90 47-53 6 3 Indiscriniin ate inean = 34" 19' 15'' •81 "Weighted mean = 34 '9 15 -Si ('= = =bO "■65. 151 observations, 27 pairs. [Reduction to A = + i''-24.] Latit 34 19 :0"-I2. 1 from latitude observa- ide. // 6 -41 6-67 6-12 6 02 4-73 4-87 4-45 5-62 7-32 6 -oS 5-65 7-15 6-17 5-14 4-73 6-51 4-42 7-40 5-70 7 -22 5 -58 6-25 4-58 5-88 6 -07 5-56 4-55 — o -60 -0-86 —0-31 — O -21 + 1 -08 -fo-94 + 1-36 +0-19 -I -51 —0-27 +0-16 -I -34 —0-36 +0-67 + 1 -oS —0-70 + 1 '39 -1 -59 4 o -II - 1 -41 +0-23 -0-44 + 1 -23 — o -07 — 026 +0-25 -M-26 302 THE EASTERN OBLIQUE ARC. 60. Sa ivnee, Georgia One division of levels I this statioi 1. Pairs c f stars. 6 583 6 644 *6 698 *6 698 6 723 6 739 6 762 6 769 6 779 6 827 6 805 6 867 6 S39 6 S56 6 88 1 6 896 6 890 6 928 6 975 6 983 7 006 7 029 7 055 7 ■■07 7 143 7 i7t 7 1 88 7 241 7 257 7 281 7 310 7 351 7 368 7 398 7 474 7 501 7 5.53 7 5«2 7 607 7 614 7 641 7 668 7 712 7 727 7 820 7 806 7 882 7 900 7 923 7 931 7 945 7 95« , — H. W. Blair. Zenith telescope No. 5. First series. October 6 to 17, 1873, ''•QO. One turn of niicronieter=4r"'429 from circutnpolar observations at Adopted mean seconds of N. P. D. // // 23-20 31 -63 57 '40 57 -40 03-41 34-50 02 -04 50-67 41 -98 01 -14 02 -QO 33 -66 59 ''3 50-15 29-63 03-28 25-31 32 -49 21 '39 29 -70 58 '44 06-66 52-05 44-24 41 -57 21 -34 56-99 05-54 55-52 03-05 2674 04-85 34-57 12-15 00-25 3' -'6 '3-72 06 -17 58-14 26 -05 3' -36 56-41 52 -43 14 -32 01 -40 25-13 I [ -16 45-36 32-07 57 -97 07-43 06 -07 Latitude. 9 5 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 34 4 04-14 +0-26 04 -QO +0-40 05 -35 -0-95 03-91 +0-49 03-62 +0-7S 03-25 + 1-15 05 -10 —0 -70 04 -18 +0-22 03 -65 +0-75 04-47 — -07 04-18 +0-22 04-69 —0 -29 04 -43 —0-03 04-73 -0-33 04-76 -0-36 03 -5« +0-82 04 -84 -0-44 04 -62 -0 -22 04 -02 +0-38 04 -63 -0-23 05-32 — -92 04 -20 + 0-20 04-13 + 0-27 04-67 -0-27 04-37 +0-03 05-22 -0 -82 Indiscriminate mean=34° 14' 04^-39. Weighted mean =34 14 04 -4o±o"-o7. (•=±o"-28. 132 observations, 26 pairs. [Reduction toA=+6"-89.1 THE ASTRONOMIC MEASURES. 303 60. Sazvficc, Georgia. — A. H. Scotl, /enitli telescope No. 5. Second series. October 30 to Novem- ber 15, 1873. One division of level = i" 'cxj. One turn of niicronuter =41" • 129 from circumpolar observations at this station Pairs of stars. 7 137 7 306 7 3«o 7 559 7 59" 7 674 7 S55 7 913 8 114 8 282 92 164 224 305 352 7 166 7 36' 7 449 7 568 7612 7 749 7 «93 7 958 8 146 8 300 142 181 227 3 '4 365 adopted stfcoiuls of mean N. P, IJ. //' 7V I,.-Uitude. V >' " / // // 45 •9" 3" '31 5 4 34 14 "3 •'•"5 + 0-30 32 '55 14 -(17 5 4 04 -61 —0-46 33 ^V 04 -16 5 4 04 -26 — o-ii 07-17 48-19 5 4 03-79 +0-36 30 '.So 42 -39 6 4 04-23 -o-o8 33 '52 27-99 6 1 03 53 +0-62 12 23 02-81 6 4 04 -QI +0-14 18 '59 06 -26 6 4 03-12 + 1 -03 42 -ir 01 -QO 5 4 04 12 +0-03 32-54 33-50 4 3 03-52 +0-63 43 ''4 36 -50 6 4 05-59 -I -44 40-52 22 -62 6 4 05 -53 -1-38 23 '05 47-09 6 4 04-88 -0-73 14 -80 '3 '77 5 4 02-95 -(-I -20 21 -iS 20-62 6 4 03-90 -fo-25 riminate mean = 34° H' 04" -13- ited mean = =34 14 04 i5zto' '•14. e= :±o" •51 82 observations, 15 pairs. [Reduction to A = -f 6" -89.] Value adopted =34° 14' 04" -20-11:0' [Reduction to A = +6" -89.] -oS. 304 6i. Aurora, Alabama. - division of level = i " '006. this station. THE EASTERN OBLIQUE ARC. -F. P. Webber. Zenith telescope No. 2. May 28 to Jnne 20, 1877. One One turn of micrometer = 45" -852 from circumpolar observations at Pairs of stars. Adopted mean .seconds of , N. P. D. " 70 Latitude. V // // / // // 4 057 4 127 t8 '90 15-10 5 3 34 08 48 -72 -1-27 4 148 4 156 59 '48 38 -60 5 3 47-74 —0 -29 4 274 4 305 05 -20 32 -60 5 3 46 -65 +0-80 4 335 4 367 21 -00 45 -50 5 3 47-59 -0-14 4 406 4 456 10 '50 15-22 5 3 46-90 +0-55 4 6S4 4 753 09 -88 43-18 6 3 46-49 +0-96 4 870 4 S76 1073 23 -05 6 3 48-73 — 1 -28 4 958 4 969 2470 18-32 6 3 48 -30 -0 -85 5 026 5 031 25-07 42 -24 5 3 49-43 — I -98 5 075 5 084 00-52 25 -75 4 3 46-56 +0 -89 5 130 5 143 56 -38 13 -00 5 3 46-94 +0-51 5 177 5 252 46 -So 03 -60 5 3 47-51 —0 -06 5 295 5 321 48 -80 13 -57 5 3 46-53 + 0-92 5 432 5 479 43 'oi 37 -63 5 3 46 -12 + 1 '33 5 502 5 587 53 '64 53 -78 5 3 48-17 —0 -72 5 834 5 927 04-50 56- 25 5 3 47-11 +0 -.u 5 937 5 991 25 -ID 21-83 6 3 47 -36 +0 -09 6 091 6 094 45 -85 26 -60 5 3 49-32 -I -87 6 151 6 203 ID -25 54-18 5 3 48 -28 -0 -83 4 242 4 303 44-50 45 -85 5 3 46 -73 +0-72 4 597 4 701 45 '45 36 -44 5 3 47-56 — Q-II 4 751 4 845 38 -25 40 -23 5 3 47-47 — -02 4 905 4 gSo 16-66 23 -48 5 3 47-14 +0-31 5 185 5 313 24-14 08 -06 5 3 47-11 + -34 5 322 5 388 10 -41 30 -48 5 3 46 -80 + 0-65 5 463 5 525 34 73 Indiscrimin 27 -79 5 ate mean = 34° 08' 3 47"-45 46-55 +0-90 Weighted mean = 34 08 47 -45 drO'-'-I2. e = ± o"-6c ). 133 observations, 26 pairs. [Reduction to A = + o"-26.] i THE ASTRONOMIC MEASURES. 305 62. , \tlauta Middle lUisi 1.S72. One division of k-vfl = tions at this station. , (ieorj^ia. -1'. I'. Webber. Zenith telescope No. 5. September 4 lo 27, \" (X). One turn of micrometer = 41" 427 from circumpolar ob.serva- I'airs of stars. Adopted seconds of mean N. V. D. «' w Latitude. V /t // / // // 6 109 6 134 2976 28 -(XJ 5 7 33 54 21 -68 +014 6 452 6 4.S7 2216 1 4 -(X) 5 7 20 -98 4-0-84 6 5H3 6 595 29 28 fxj -70 5 7 21 -48 -^0-34 6 656 6 676 36 16 38-4' 5 7 21 -80 -J-0 02 6 697 6 724 3 1 'So 22 20 5 7 22 -15 -0-33 6 739 6 763 42 25 15 73 5 7 22 03 — 0-2I 6 777 6 800 53 -So 5470 5 7 20 -64 -(-I -18 6 S39 6 S81 08 -50 41 '09 5 7 20 -96 + 0-86 6 92.S 6 952 44 '30 25-72 6 7 2' 53 ^ 029 6 97S 7 "27 00 ■ 1 55 '03 5 7 22 -91 — I -09 7 061 7 "67 4470 26-26 5 7 21 -63 -0-19 7 164 7 213 4,S -05 43 -'5 5 7 21 -99 -0-17 7 336 7 368 43 '24 49 '3 1 5 7 21 -60 -t-O-22 7 431 7 450 32 -92 40 -lo 5 7 21 62 4-0 -20 7 520 7 548 21 -88 50 '34 5 7 21 -41 -1-0 -41 7 602 7 607 13-42 14-82 _ 5 7 22-47 -0-65 7 631 7 664 15 -78 31 -'5 5 7 21 69 + 0-13 7 695 7 712 '675 09-92 5 7 20-63 + 1 -19 7 754 7 796 47 -44 19 -82 5 7 21 -74 +0-08 7 880 7 914 39-28 35 '30 5 7 21 -75 4-0-07 7 94S 7 958 4' 79 25 'oiJ 5 7 21 -86 — -04 S 032 8 037 39-'i 55-81 5 7 20 ■ 60 + 1 -22 S 054 8 071 iS -20 1 6 60 5 7 21 -52 -0-30 8 115 8 131 33 -68 36-09 5 7 22 -19 -0-37 8 203 8 224 25 61 06 67 5 7 22 -24 -0 42 8 250 8 26S 44-62 39 20 5 7 21 -67 + 0-15 8 330 s 370 26-62 57 '53 5 7 22 -46 0-64 63 S3 36 -22 45-87 5 7 20 -84 -0-98 120 158 30-40 18-53 5 7 22-44 — 62 168 '97 25 29 16 -07 5 7 21 -51 + 0-31 6 475 6 542 18-47 44-58 5 7 21 -69 -0-13 6 678 6 721 57 'oS 47 -84 5 7 22-41 -059 6 745 6 758 33 '62 58 -97 5 7 22 22 — 0-40 6 7S0 6 805 l6-12 11 -64 5 7 21 69 +o-:3 6 865 6 868 27-14 54 -36 5 7 21 -31 -0-51 6 962 6 975 14-50 32 '3" 5 7 22 07 -025 7 "41 7 "7 46 -98 37 15 6 7 21 00 + 82 7 "46 7 '53 35 '47 23 -88 5 7 22 44 —0-62 7 166 7 223 42 -98 55 -00 5 7 22 03 — -21 7 256 7 260 40 -85 00 -03 5 7 21 -54 -TO 28 7 350 7 417 57 -93 02 dx 5 7 21 -71 -t-OII 7 4,S3 7 465 "4 '57 01 -52 5 7 22 -77 — -Q.S 4192— No. 7 — 02- 20 io6 THE EASTERN OBLIQUE ARC. Atlanta IMiddle Base, Georijia — continued. Pairs o f stars. Adopted seconds of mean N. P. D. „' ■"■' Latitude z/ // // / // // 7 544 7 571 23 '41 32 -50 5 7 33 54 21 -55 4-0 -27 7 668 7 674 13-61 55-06 6 7 21 -96 —0 -14 7 727 7 733 31 '64 00-75 5 7 22 -27 -0 -45 7 901 7 923 55 06 50-55 5 7 22 -36 -0 -54 7 937 7 995 25 '96 57 ■S8 5 7 22 •87 - ' -05 8 052 s 076 19 "57 34 -05 5 7 22 -33 "O-51 8 125 8 147 36 '34 32-05 5 7 21 -55 +0-27 8 212 S 284 08 -20 II -50 5 7 22 -37 - -55 8 300 8 364 53-12 50-24 6 7 21 -13 -| -69 54 lOI 40 -84 57 -45 5 7 22 -45 —0 -63 152 178 04 -34 22-39 5 7 22 •32 —0 -50 198 217 59 -42 Indi.scriniina 28-50 te mean ^ 5 1 -lO 1-1' oj 54 / 2l''-82 22 •09 -0-27 ■Weighted mean = 33 54 2 r -82 ±o''-05 c = ±o''-3 5 274 observations, 54 pairs. [Red notion to A = ^-o" -40.] 63. Atlanta, Georgia. — C. H. .Sinclair. Meridian telescope No. 13. January i to 22, 1880. One division of level = 2" "] at 33° F. and 2" -64 at 75° -2 F. One turn of micrometer = 77" -783 from circuripolar observations at this .station. Pairs of stars. 522 628 682 S19 897 974 I 006 I 065 (557) I 139 I 214 I 254 I 301 I 307 I 382 I 409 I 460 (772) I 500 Adopted seconds of mean N. P. D. 08 -80 44-71 28 -85 50-72 26 -10 43 -72 08 -58 32-79 52 -20 03-10 58-22 55 -50 25-50 53 -25 17-50 55-20 29-50 04 -80 32-12 Indiscriminate mean = 33° 44' 59'' -34. Weighted mean =33 44 59 30 (' = zb o" -50. 93 observations, 19 pairs. [Reduction to A = + o" -08.] 592 00 'OO 657 49-20 706 13 -04 842 12-40 921 25 -63 981 56 -90 I 052 02 -67 I 087 55 -So I 129 37-76 I 192 07 -20 (654) 14 -60 I 272 34 -60 I 346 05 -68 I 365 42-75 I 393 oS -00 I 424 33 -So X 456 43 -50 I 492 22 -02 I 504 03-40 Latitude. o / // 33 44 58 -83 58-42 59 -3^ 59-25 5S -63 60 -44 59-5S 58-99 59-12 59 -48 58-19 60-51 58-30 60-26 58-92 59-45 59-66 61 -14 58-85 d= 0-I2. +0-47 +0-8S — o'oS +0-05 +0-67 -I -14 — o -28 +0-31 +0-18 -o-i8 + I-II — I -21 + 1 -OO — o -96 +0-38 -0-15 —0-36 -1-84 +0-45 THK ASTRONOMIC MEASTRES. 307 64. A'a/ialiiur, Alahaiiia. — (). ]'.. I'Vciich. /eiiilh Iclescojjc- Xo. 2. June 3109, 1898. One division of level = i""2i I, as determined by K. (>. I'ischer, 1.S91. One turn of micrometer = 46"'376 from latitude ohserNations at this station. I'aii's ol slar.s. 1| 4 729 *4 74S *4 748 4 762 *(2 232) *(2 237) 4 830 4 873 4 936 4 967 (2 350) *5 098 *5 098 5 143 5 iSi 5 287 (2 4S6) 5 3SS 5 509 4 741 *(2 232) '"(2 237) *(2 237) *4 792 *4 792 4 847 1- 4 9071' 4 939 (2 339) (2 358) (2 396) ■(2 399) 5 155 5 216 *5 322 *5 322 5 462 5 523 A(l<)]He(l seconds of mean N. P. U. 11' w LatiUulc. V // // / // // 1 1 "45 36-36 4 >3 33 13 39 '87 +0-03 38 -32 04-04 2 5 39-49 +0-41 38-32 56 -63 4 7 39 45 +045 18-51 56-63 2 5 38-99 +0-91 04 -04 14-73 2 5 40-45 -055 56 -63 14-73 4 7 40 -07 -0-17 12-97 40 -08 4 13 39-95 —0-05 13 70 36 -85 5 14 39 -80 +0-10 39-62 5' -24 5 14 3972 ^o-i8 41 -07 32-25 5 14 40 -29 -039 47-42 21 -87 4 12 40-54 —0-64 33-99 53-58 4 9 39 -58 4-0 32 33-99 09 15 3 S 39 -78 --0-12 3' -89 04-40 4 '3 39 '40 —0-50 38 -78 32-52 4 13 40-43 -0-55 51 -95 44-83 4 9 40-30 —0-40 44-46 44-83 3 3 39-60 +0-30 59 "76 56-50 4 '3 39 -60 -0-30 17 '33 38-06 4 >3 39 "92 -0 -02 criminate mean = ■,-,0 13' 39" ■85- tited mean = 33 13 39 -90- o''-o6. c — ±0 "■31- 71 observations, 19 pairs. [Reduction to A =i-o"-39.] 65. Montgomery, Alabama. — G. W. Dean. Zenith telescope No. 5. March 22 to division of level = a" "929 as determined at this station. One turn of micrometer circumpolar observations at this station. Adopted seconds of mean N. P. D. 28, 1S56. One = 41" -45 from Pairs of stars. 3 '09 3 '12 3 '40 3 '76 3 202 3 220 3 241 3 255 3 307 3 327 3 33' 3 352 3 399 3 423 3 5 '5 3 522 *3 545 3 548 *3 545 3 560 3 580 3 621 *3 634 3 665 11 -iS 07 13 14 -oS 17-90 16 72 42-66 46 -01 48-07 18-20 55 ■ 1 1 54 'o>i^ 00 -86 39-20 29-80 16 -10 00-00 26 -90 16-96 26 -90 19-90 57 -So 23-07 27 -20 27 00 11' 7V Latitude. :• / // /' 5 14 32 22 45 -66 -0 25 5 14 45-68 -0-27 5 14 45 19 + 0-22 4 13 45«4 •0-27 4 13 44-34 •i-i 07 4 '3 45-42 — o-oi 4 13 45 95 - 54 6 14 45 93 - 52 6 lO 45-09 - -32 6 10 44-89 - 52 6 14 45 "35 -rO-06 5 9 44 -So - -61 I 3o8 THE EASTERN OBLIQUE ARC. 65. Mo'iti^oincry, Alabama — continued. Pairs of stars. Adopted seconds of mean N. P. D. w 7C Latitude. V // // / // // *3 634 3 670 27 -20 ' 5 -40 5 9 32 22 44-96 +0-45 3 704 3 736 23 '04 50 -53 6 14 45 -86 -0-45 3 760 3 776 44 '44 55 -07 5 14 45 -38 +0-03 3 S25 3 837 26-18 07-13 5 ■4 45 -81 —0 -40 3 885 3 911 38 '35 24-17 5 14 45 -15 +0 -26 3 931 3 954 09 -98 08 -27 5 14 45 -75 -0 -34 3 964 3 973 52 -30 42-17 5 14 45 -41 -oo *3 990 4 057 51 -22 19-75 5 9 45-14 +0-27 *3 990 4 059 51 '22 37 -41 5 9 45 -60 — -19 4 079 4 121 05 -62 49-60 5 '4 45-64 -0-23 4 127 *4 1 88 13-94 55 -48 4 9 45 -66 --0-25 4 184 *4 188 2576 55 -48 5 9 45 -56 -0-15 4 203 4 229 22 -14 39 -46 5 14 44-72 +0 -69 4 240 4 258 37-09 56 "60 4 13 45 -67 — -26 4 2S7 4 351 1 8 -35 47 -80 5 14 45 -40 -f -01 4 384 4 390 46 -34 04 -56 5 14 45 -67 —0-26 4 421 4 457 26 -53 52 -70 5 '4 44-95 +0-46 4 468 4 538 38-73 47 -78 5 H 44 -80 -t-o -6r 4 553 *4 596 03 -'6 14-57 5 9 45-69 -0 -28 4 566 '■'4 596 23 -37 '4-57 5 9 45 -10 +0-31 4 609 4 618 52 -22 10-25 5 14 45-26 ^0-15 4 632 4 640 28-1,3 29-75 5 14 45 -66 -0-25 4 694 4 714 35-61 32 -09 2 9 45 -66 -0-25 4 699 4 729 32-67 57-47 2 9 46 -01 —0 -60 4 753 4 827 53-46 50-70 2 9 45-94 -0 -53 4 789 4 853 55 -76 58-71 2 9 46-03 —0 -62 4 902 4 96 r 08-17 41 -02 2 9 45-50 — "og 4 993 5 026 17 -16 38-94 2 9 45-80 -0.39 Indiscriminate mean = 32° 22' 45'' -43. "Weighted mean • =32 22 45 -4i=bo"-o4. e = ± o" -29. 181 observations, 40 pairs. [Reduction to [^ or center of State House = -j- o" -22.] THK ASTRONOMIC MEASURES. 309 66. /. owe r Peach 7>rd', Alabama. -\i. (ioodfellov^ , Zenith li- One division of level =0''' '99 from ob.servation.s at this station, from circiimpolar ob.servationH at Mobile, Alabama. U-seope No. 5. April 4 to 16, 1S57. One turn of micrometer = 41''' '481 P.'tirs (if stars. 2 740 2 841 2 912 2 995 3 047 3 095 3 140 3 246 3 278 3 355 3 406 3 505 3 545 3 610 3 661 3 691 3 725 3 862 3 915 3 981 *4 017 *4 017 2 792 2 S60 2 952 '3 "75 ''"3 "75 3 lo^ 3 228 3 265 3 34' 3 399 3 421 3 522 3 602 3 650 3 685 3 729 3 788 3 885 3 952 3 995 4 027 4 072 Acloi)te -o-i8 1 445 468 50-53 47-40 6 6 33 "52 —0 -lo I 492 528 41 -55 34-60 6 6 34 -50 -:-o8 I 557 *] 609 02 -42 13-00 7 4 32 -83 +0-59 I 59f *I 609 27 -12 13 -oo 5 4 32-43 +099 I 629 *I 64S 33-21 36 -54 6 4 33-67 -0-25 I 632 *I 64S 34 -83 36-54 6 4 32-91 -ro-51 I 669 768 45-50 52 -88 6 6 33-15 -0-27 I 845 925 56-45 28 -05 6 6 33-32 + 0-I0 I 935 951 05 -36 10 -19 6 4 33 20 -^0-22 I 935 2 016 05-36 54-31 6 4 33 -48 —0-06 2 067 2 155 47-13 13 -70 6 6 34-29 -0-87 2 182 2 228 33-06 16 -11 5 6 33-57 -015 2 306 2 409 28 -40 10-93 6 6 34 -37 -0-95 2 423 2 429 19-10 18-03 4 5 33 -37 +005 2 441 2 444 28-79 oS -55 6 6 33-17 -^025 2 463 2 563 34-28 05-83 6 6 34-38 —0-96 111 liscriiiiiiiate mean =30° 41' 33" 43- W ;ij!;hled mean = 30 41 33 -42 ±o"-o6. <'= ± o"- 46. 25' ^ observations 43 P<»*-s- [Rt iduction to A (Episcopa 1 Church. ')= - io"-72.] 312 THE EASTERN OBLIQUE ARC. 69. iT(75/ /'(75r(roo«/(r, Mississippi. -R. H. Fauntleroy. Zenith Telescope No. r. June 25 to July 26, 1847. One division of level = o" '90. One turn of micrometer = 45" '502 from latitude observa- tions at this station. Pairs f stars. Adopted mean seconds of N. P. D. n' w Latitude. 7' // // / // // 5 463 5 563 ID -60 57-00 2 12 30 20 41 -19 -0-27 5 628 5 724 I 2 -36 17-13 I 6 40 -87 +0-05 5 667 5 749 50-65 oi -25 3 '9 40-43 +0-49 5 795 5 940 39 77 '9-77 2 12 40-79 +o-'i3 5 S02 5 853 29 78 31 -96 2 12 40-91 +0 -01 5 953 6 006 12 '40 19 -20 3 19 40-57 +0 -35 6 013 6 094 44-92 09 -65 2 12 41 -08 —0 -16 6 052 6 143 49-24 12 -lo I 6 40 -82 +0 -10 6 155 6 2i5 39 79 44-99 I 6 40-44 +0-48 *6 224 6 4r8 14-98 57-12 3 12 41 -71 -0-79 *6 224 6 420 14-98 29-64 3 12 40 -60 +0-32 6 269 6 373 23 -53 48 -06 4 24 4r -51 -0 -59 6 42S % 615 18-42 13-29 4 12 40-70 ■f -22 6 476 % 615 46 -40 13-29 3 9 40-62 +0 -30 6 460 6 5-^3 27-50 59-08 2 8 41 -26 -0-34 6 626 *6 644 42-71 42-24 3 12 • 40 -76 +o-i6 *6 644 6 717 42 -24 07 -50 3 12 40 '80 +0 -12 6 720 6 744 17 -06 27 -39 . 3 '9 40 -98 —0 -06 6 748 6 833 58 -80 17 -10 3 '9 40-32 1 -60 6 772 -6 865 20-15 23-86 3 12 40-67 f 0-25 6 805 ^^•6 865 48 -38 23-86 3 12 41 -lo — o-i8 6 891 6 932 53 -88 5' -27 4 24 40 -85 +0-07 6 910 6 970 51 -61 01 -18 3 19 40 -18 ^-0-74 6 985 7 088 I' 75 47 -30 4 24 40-52 ■ + 0-40 7 062 7 223 18-98 24-77 3 '9 40 -68 +0-24 7 091 7 257 37-60 47-3' 3 '9 40 -78 +0-14 7 125 7 182 09 -ro 26 -39 5 29 41 -22 —0 -30 7 215 7 269 04-05 25-4' 5 29 40-51 +0-41 7 324 7 401 35-18 34-71 2 12 41 •21 —0-29 7 350 7 448 53 "53 56-16 3 '9 41 -16 -0 -24 7 476 7 527 50 -78 29-07 4 24 41 ■\\ —0 -22 7 488 *7 561 47-00 25 -73 3 12 40-63 + -29 7 589 "7 561 08 -90 25 -73 3 12 40-24 + 0-68 7 642 7 662 28 -69 31 69 3 19 40 -69 +0-23 7 606 7 705 22 -40 41 -54 2 12 41 79 — -87 *7 689 7 754 12-97 12-49 3 12 41 -42 0-50 *7 689 7 77« 12-97 04-36 3 12 41 -42 0-50 *7 766 7 795 51 -04 22 -52 2 8 41 -oo - -08 *7 766 7 809 51 -04 42-31 I 4 41 -72 -0 -80 7 812 7 827 16-86 10-45 3 19 41 -24 -0-32 I Pairs of stars. 7 -'^45 7 9'2 7 888 7 908 7 953 7 99^ 7 975 8 115 8 036 8 149 « "53 8 218 8 262 8 282 8 322 8 33' THE ASTRONOMIC MEASURES, 69, luxst /'asrni^oiiUi , Mississippi — rfuilimu-d. Adopted seconds of mean N I'. I). 3^3 29 '35 51 70 36 -03 56-60 23 -.6 27 29 43 ■ ' 2 25 -60 09 ■ y f 43 -83 17-58 46 -45 42 75 1 1 -98 42 -55 01 -65 11' w Latitude. V / // // I 6 S"-' 20 41-39 -0 -47 4 24 40 96 -0 -04 4 24 4' '^7 -075 I 6 40 -68 i 0-24 3 19 41 -04 -f) -12 I 6 40-35 ^0 -57 2 12 40 -59 +0 -33 2 12 40 93 —0 -01 I Iiidiscriiniiiale iiiciin = 30° 20' 40" '92. Weifjhtt'd iiit-an = 30 20 40 -92 +: o" -04 I? = rtr o" -39. 129 oh.servations, 48 pairs. [Reduction to A = o" 'no.] 70. Fori Morgan, Alabama. — R. H. Fauntlero)-. Zenith telescope No. i. March 1847. One division of level = o" -91 from observations at this station. One tnrn = 45" -570 from latitude observations at this station. 23 to April 30, of micrometer fairs t f stars. Adopted seconds of mean N. P. D. «' ?<■ Latitude. V // // / // // 2 650 2 673 34 -45 58-17 4 24 30 13 47-92 -0-03 2 725 2 765 32 42 38 -CXI 4 24 48-22 -0-33 2 844 2 889 22 -03 oa -70 4 24 47-91 — -02 2 970 3 <75 57 ■<>3 33 -87 4 24 48-08 —0-19 3 105 3 140 59 -36 03-52 7 42 47-75 +0-14 3 -82 3 25' 31 '55 45-44 8 48 47 -78 -f o-ii 3 325 3 368 42 -30 44-12 10 59 47-96 —0-07 3 402 3 532 33 ■40 33 -90 '3 77 47-67 +0-22 3 592 3 682 '9 97 44 -80 15 9" 48 -20 -0-31 3 758 3 843 ■7 75 32 -04 16 100 47 -52 +0-37 3 868 .1 910 42 -68 32-3' 13 77 48-13 -0-24 3 949 3 979 02 -56 29 -34 14 83 48 -oS —0-19 4 094 4 123 33 95 w 95 1 1 67 47-66 +0-23 4 228 *4 303 34 -28 52 92 10 59 47-92 —0 -03 4 271 •'^4 303 12-79 52-92 10 59 48-10 — 0-2I 4 341 4 423 20-69 42 -65 8 48 47 -73 + 0-16 4 596 4 637 31 -28 38 -80 7 42 47 -84 + -05 4 699 4 737 56 67 33 -72 5 30 47-67 -1-0-22 4 792 4 874 20 -54 04 -89 ^> 18 47 -91 -0 -02 Ii idiscriininate mean = 30^ 13' 47 " -9<-). \ l^eighted mean = 30 '3 47 •894, 0" -03. f = rt "-4.. If 16 observations, 19 pal rs. [Re. Inction to A = 0" CKl. 1 314 THE EASTERN OBLIQUE ARC. 71. AVttv OrA'rt;/.?, Louisiana.— J. Kincheloe. Zenith telescope No. 5. January r6 185S. One division of level =o'''845 from observations at this station. One turn = 4i'''5i6 from circumpolar observations at this station. n' w Latitude. to February 10, of micrometer Pairs of stars. 707 727 745 749 766 772 806 *905 885 -905 -981 999 *98i I 034 I 066 I 084 1 107 I 123 I 221 I 269 'i 323 J 335 'I 323 I 343 I 376 I 414 I 449 I 476 I 492 I 527 I 571 I 602 I 631 I 651 I 69C3 I 778 I 834 •■■■I 897 I 862 *i 897 I 935 I 970 'I 981 2 014 -I 981 2 021 2 084 *2 155 2 090 *2 155 2 200 2 228 2 237 2 254 2 30' 2 340 -2 440 2 464 '2 440 2 485 -2 504 2 5'4 -2 504 2 551 2 639 2 691 2 73' 2 79« 2 892 2 97' 3 000 ■■■3 016 3 002 ■■3 016 3 035 3 075 3 >23 3 162 3 '«2 3 227 .'Adopted seconds of mean N. P. D. // // 28 -20 01 -40 05 -00 04-29 47-04 06 -90 39 '33 32 -23 19 '58 32 -23 51 -91 04 -94 51 '9' 04 -3 > 1274 13 -68 43 '34 54-32 04 -42 09-78 41 '66 43 -73 41 '66 44-52 17-23 52 -9S 09 '60 59-92 28 -29 37 -70 13 '98 IS -08 54 '99 03 -30 59 '50 1 2 -50 21 76 52 -84 04 -98 52. 84 04 -66 28 -33 ] I '46 28-15 II '46 2,S -61 20-45 18 -90 07 -88 1 8 -90 ID -lO 23 -24 19 -61 03 -50 43 '35 34 -80 30-55 13 -88 30-55 16-34 '5 -25 33 -86 15-25 55 -30 01 -88 10-23 II -66 29 -84 40 -62 46-44 39 -43 09 -33 46-66 09 '33 02 -40 06 -70 46-78 56 -49 16-62 38 -06 5 29 57 25-17 +0'II 5 24 -43 +0-85 5 24 -73 + 0-55 4 24 -61 +0.67 4 24 -66 +0-62 4 26 01 -0-73 4 25-30 — '02 5 24-90 + 0-38 5 25-29 — -Ql 5 25 -39 — -11 4 26 -35 — I -07 4 25-30 — -02 5 25 -50 — -22 5 25 -70 —0-42 5 24 -06 + 1. 22 5 25-83 -0 -55 5 24 -88 -I-0-40 5 24-16 + 1 -12 4 25 -88 — "60 3 24-89 + 0-39 5 24-43 + -85 4 26-05 -0-77 3 26-45 -I -17 4 25 -60 -0-32 4 26 -17 -0-89 5 24-72 +0-56 5 25 -72 -0-44 5 25-51 -0-23 4 25 -66 -0-38 4 24 -43 +0 -85 4 25 -23 4-0-05 4 24-42 +0 -86 5 26 -oi - 0-73 5 26 •r4 -0-86 5 25 -25 +0 -03 4 24-97 +0-31 4 25-29 - -01 5 26-03 -0 -75 5 25 -58 —0 -30 5 24 -87 i 0-41 THE ASTRONOMIC MEASURES. 315 71. New Orleans, Louisiana — continued. Pairs of stars. S 242 .■^ ,V3 3 35S 3 3^1 3 2S6 3 327 3 359 3 39« 'Adoptee mean seconds of N. P. D. «' // // 41 74 4678 6 35 -86 2975 6 29-64 37 -80 4 43 '32 44-40 6 w Latitude. V / // // 5 29 57 26-12 -0-84 5 24 -02 + 1 -26 5 25 '35 ~o o-j 5 25 -56 -0-28 Indiscriminate mean = 29° 57' 25'''-29. Weijfhted mean =29 57 25 -28^0" -07 e = ±L 0^-43. 256 ob.servations, 44 pairs. [Reduction to ^^ = o^'-ckj.] 3. SUMMARY OF RESULTS FOR LATITUDE. No. Name of station. State. Resulting latitude. Probable error of result. / // // 1 Calais Me. 45 I 1 09 40 =!zO-o6 2 Cooper Me. 44 59 12 -60 005 3 Humpback Me. 44 5" 47-56 0-05 4 Bangor Me. 44 48 1 2 -87 005 5 Farmington Me. 44 4" 19 '54 005 6 Mount Harris Me. 44 39 54-66 004 7 Howard Me. 44 37 49 '24 005 8 Mount Desert Me. 44 21 06-51 003 9 Ragged Mountain Me. 44 12 42-96 004 10 Sabattus Me. 44 oS 37 73 09 II Mount Pleasant Me. 44 01 36-44 0-04 12 Cape Small Me. 43 46 43 69 0-04 13 Mount Independence Me. 43 45 34 -47 006 14 Gun.stock N. H. 43 31 03 Si 0-05 15 Agamenticus Me. 43 13 24 96 006 16 Isles of Shoals Me. 42 59 12-97 009 17 Unkonoonuc N. H. 42 58 59-34 ^o^ 18 Thompson INIass. 42 36 38 "02 010 19 Wachusett INIass. 42 29 16-13 -04 20 Cambridge, Harvard College Observatory Mass. 42 22 48-05 022 21 Cambridge, Cloverden Observatory Mass. 42 22 40 -97 0-08 22 Mount Tom Ma.ss. 42 14 27 62 006 23 Manomet ISIass. 41 55 35 '35 005 24 Sandford Conn. 41 27 40-47 o-oS 25 West Hills N. Y. 40 48 50 -06 0-04 26 New York X. Y. 40 43 48 -39 009 27 Beacon Hill N.J. 40 22 27 -Si 0-07 28 Mount Ro.se N.J. 40 22 05 -41 oS 29 Yard Pa. 39 58 29-39 006 * Center of dome. 3^6 THE EASTERN OBLIOl^E ARC. 3. SITMINIARV OF RESULTvS FOR L .\TITITDE- -continuei , No. Name i}i station. State K esult atitu niii I'robable error de. of result. / // // 30 Priiicipio Md. 39 35 32 -81 ±0 -04 31 Maryland Heitjlits Md. 39 20 32 -10 -04 32 Pooles Islaiiil Md. 39 17 ■7-52 0-15 33 vSugar Loaf Md. 39 15 4971 -K) 34 Dover Del. 39 09 13 -62 -06 35 Webb Md. 39 "5 25 -21 -04 36 Soper Md. 39 05 10 -69 -09 37 Rockville Md. 39 05 'f45 0-03 38 Taylor Md. 38 59 46 -oS -12 39 Strasbury; Va. 38 59 31 '49 0-09 40 Cape Ma\- N.J. 38 55 44 74 -06 41 Causten, Washington D. C. 38 55 32-18 G -06 42 Naval Observatory (new), Washington* D. C. 38 55 13-91 -06 43 Hill Md. 38 53 52-31 0-05 44 Naval 01)servatory (old). Washington t D. C. 38 53 38 -79 0-03 45 Seaton, Washington I). C. 38 53 25 -20 0-15 46 Coast and Geodetic Snrvej- Office, Washington j D. C. 38 53 07 -43 -02 47 Bull Run Va. 38 52 56-79 -07 48 Marriott Md. 38 52 25-12 -06 49 Cape Henlopen Del. 38 46 40 -00 0-05 50 Clark Va. 38 kS 39 -80 -06 51 Elliott Knob Va. 38 09 57-51 -11 52 Charlottesville Va. 38 02 00-95 0-14 53 Long Mountain Va. 37 17 28-72 -09 54 Moore N. C. 36 23 54-95 -09 55 Young N. C. 35 44 21 -50 -12 56 King N. C. 35 12 13 -31 -07 57 Paris vS. c. 34 56 3 I -96 0-07 58 Currahee Ga. 34 3' 37 '75 -oS 59 Lavender Ga. 34 19 15-81 012 60 Sawnee Ga. 34 J4 04 -20 0-08 61 Aurora Ala. 34 08 47-45 0-I2 62 Atlanta Middle Base Ga. 33 54 21 -82 0-05 63 Atlanta Ga. 33 44 59-30 (1-12 64 Kahatchee Ala. 33 13 39 -90 -(-)6 65 Montgomery Ala. 32 22 45 -41 -04 66 Lower Peach Tree Ala. 31 50 21 -19 -10 67 Coon Ala. 31 '4 47 -82 -05 68 Mobile Ala, 30 4' 33-42 -06 69 East Pascagoula Miss. 30 20 40-92 -04 70 Fort Morgan Ala. 30 13 47 -89 0-03 71 New Orleans La. 29 57 25 -28 0-07 * Center of clock-room. f Center of small d ome. t station in yard. B. THE RESULTS FOR LONGITUDE AT THE ASTRONOMIC STATIONS OF THE OBLIQUE ARC. I. GENERAL STATEMENT. Connected with the arc there are fourteen well determined lon^i^itude .station.s avail- able for comparison of geodetic and a.stronomic longitude.s. The station.s are marked by their appropriate sign on the general Map B (in pocket), and are irregularly dis- tributed over the region of the arc. Within the limits of the city of Washington there are four longitude .stations, all within a few kilometers of one another, and consequentl)- under the same general influence of zenithal deflection. The.se four stations have been treated as one in this di.scussion. The following stations are common to the arc of the parallel in latitude 39° and to the oblique arc: Cape Ma}-, New Jersey; Dover, Delaware; three* of the Washington, District of Columbia, .stations; Stra.sburg, \'irginia, and Charlottesville, Virginia. The longitudes here given depend on the standard longitude system of the United States, as presented in the Report of the U. vS. Coast and Geodetic .Survey for the year 1897, Appendix No. 2, " The telegraphic longitude net of the United .States and its con- nection with that of Europe, 1866-1896.""!' (pp. 197-261.) Six of the arc stations are standard stations, i. e., Calais, Maine; Cambridge, Mas.sa- chusetts. Harvard Observatory; Cape May, New Jersey; Wa.shington, District of Colum- bia, Naval Observatory (old); Atlanta, Georgia, and New Orleans, Louisiana. For these stations, particulars and full abstracts of the individual results are given in the Report for 1897. It .suffices, therefore, to present only the dates and results at these stations, but for the remaining stations, abstracts are given to the .same extent as in the Report for 1897, together with all necessary explanation. In nearly every case of a telegraphic determination of a difference of longitude the ob.servers exchanged places after one-half of the proposed olxservations had been made, in order to effectively elimi- nate differences of personal equations. All these longitudes count from Greenwich, positive to the westward. The prol)al)le error of anj- one of the adjusted standard longi- tude determinations is ±o''o5, and none of the probable errors of the longitudes used in this discussion exceeds dczo^'og. *A fourth, named Seatoii (ea.st of the United .States Capitol), established in 1S49. was not a station of sufficient importance to be included in the general longitude net. fKor an abstract of this paper see Gould's Astronomical Journal, No. 412 ^September 14, 1S97). 3i8 THE EASTERN OBLIQUE ARC. 2. RESULTvS FOR LONGITUDE PRPIVIOUSLY PUBLISHED. Results for longitude of stations forming part of the standard longitude net of the United States or elosely eonneeted thereivith . [Taken from Coast and Geodetic Survey Report for 1897, p. 254.] Name of station. Point of reference. Longitude west of Clreenwich. /;. VI. S. ° ' " Calais, Maine. Transit. 4 29 07 -857 67 16 57 -86 Caniljridtje, Massachusetts. Dome of Harvard College Observa- 4 44 31 •046 71 07 45 '69 tor}-. Cape May, New Jersey. Transit. 4 59 43 '045 74 55 45 '68 Washington, District of Columbia. Dome of old Naval Observatory. 5 08 I2'r53 77 o,^ 02-30 Atlanta, Georgia. New I )rleans, Louisiana. Tran.sit, 1S96. 5 37 338 «4 23 20 -07 Transit, 1880 and 1895, Lafayette 6 00 16763 90 04 II '44 vSquare. Charleston, vSouth Carolina.^- Citadel Square, tran.sit. 5 19 44 '076 79 56 01 '14 Prom the .same Report we have t\\'o more of the Wa.shington ,station.s, pp. 257-259. and 261. Name ot station. Point ot relerence Longitude west of Greenwich. h. 1)1. S. o , ,, Washington, District of Columbia. Clock-room, new Naval Observatory. 5 08 15784 77 03 5676 Washington, Di.strict of Colitmbia. Coast and Geodetic Survey Office, 5 08 01 709 77 00 25 '64 transit. Results for longitude of stations in the .Ire ef the Thirty-ninth /'arallel. Name of station. Point of reference. Dover, Delaware f Strasburg, Virginia! Charlottesville, Virginia 1 Transit, 1897 Transit, 1S81 McCormick Ob.servatorv Longitude west of f.reenwich. /;. W. ,?. ° " " 5 02 05-230 75 3r 18-45 5 13 26-380 78 21 35-70 5 14 05 -340 78 31 20-10 3. ABSTRACTS OK RESULTS FOR DIFFERENCE OF LONGITUDE AND ADJUSTMENT OF THE LONGITUDES OF THE REMAINING STATIONS X CONNECTED WITH THE .ARC. UIHFERKNCE OF LONGITUDE BETWEEN BANGOR.'^. ME., AND CAL.-l/S. Mlv Date. Observers at 1857. Bangor. Sept. 18 23 , E. Goodfellow 25 26 Oct. 10 G. W. Dean 12 17 Difference of lonj^itude. Calais. G. W. Dean E. Goodfellow w. 5. 6 00 -275 Means 6 00 -275 6 00 -357 Bangor (transit) west of Calais (transit). Longitude of Calais, Longitude of Bangor (transit), 00-330 00 -268 00 -229 J 6 00-341 00 -362 [ 00 -367 I //. in. s. s. 6 00 -316 ±0-015 4 29 07 -857 ± o -05. 4 35 08-173. in. s. 6 00-316 * 'I"his result is added because it i.s needed further on. t These stations are included in the discussion of the arc of the 39th parallel and all nece.ssary details are published in Coast and Geodetic Survey Special Publication No. 4, " The Transcontinental Triangulation," Washington, D. C, 1900. t Published for the first time. J The longitude of this station was differentially determined from Cambridge, Massachusetts, in November and December, 1S51, lint the result was found to be weak and un.satisfactory. the observers not interchanging places, hence no use was made of those observations. THK ASTRONOMIC MEASURES. 319 DIFFERENCF, OF LONGITrDK HICTWKHN SF.ATihW STAT/ON* WASHINGTON- o/i.s/cA'yAroA'i'ioi.i)). wAsiiiNr/roN. n. c. I». C. AM) .VAI^A/. June Date, 1867. From stg western nals. I'rom sig eastern lals. W.-K. Mean western and eastern ■ignals. .( V. 5. le 4 12 •70 12 ■67 + -03 t2 •6S 6 ■6() •60 -(X) ■fx> 10 •7c •69 +0 -oi •69 1 1 ■63 •61 + 0-02 •62 21 75 •69 + '06 •72 29 •6S •69 —0 'OI ■69 Mean 12-667 Observers: G. W. Dean, in charge of party, E. Goodfellow and other observers; three were engaged in the work at the Naval Observatory and two at Seaton, but no interchange of obser\-ers took place. The results were corrected for the personal equation of the obser\-ers derived from obser- vations made for this purpose. Naval Observatory (Meridian Circle) west of Seaton (transit) Reduction to center of dome at Observator}^ Diflference of longitude Naval Ob.servatory (old) and Seaton, transit Longitude of dome, Naval Observatory (old) 5^' Longitude of Seaton ( transit ) 5 Same, as adjusted 5 12* ■667 inO' -013 —0 ■033 12 -634 iho" -013 oS" 12' ■153 07 59 ■519 "7 59 ■520 DIFFFRENCp; OI-' LONGITUnK UlsTWKKN .ST.! TESl'ILLE. X. C, .\NI) W ASH [.XGTOX. D. C. Date. 1878-79. Dec. 19 23 24 25 Jan. Observers at— Statesville. Washington. •E. Smitl G. W. Dean From west- From east- ern or ern or Statesville Washing- signals, ton signals. •.S8 •42 Mean of DitTereiice ,y _,. western Personal of longi- Weights ■49 •57 -.SI o'07 -0-05 o "07 o'o6 and east- eqnation. ern signals. s. I — o'o6 Weighted mean G. W. Dean E. Smith 15 22 '48 15 22 42 o'o6 ■44 ■39 '05 .^2 •20 0-03 Weighted mean m. 5. 15 22 -ss ■56 •4fi ■,=;-t 15 22 54 15 22 -.IS ■42 ■,^0 15 22-42 4-0-06 statesville (transit), west of Washington (transit), Reduction to center of dome at the old Naval Observatorv. Statesville (transit) west of the dome of old Naval Ol)st'rvatorv, Longitude of dome of old Naval Observatory, Longitude of vStatesville (transit), tmle. J/1 1 »t .V. 15 22 52 •50 •40 •48 15 22-51 •48 ■3S 15 22-477 gilts. Differ- ence. . s. -fo-04 3 -1-0 -02 6 — 0-08 6 O'oo 9 16 O' j-n, 22' "477 ^o -124 O 15 22 -box 5 (.\S 12-1 53 5 23 34 -754 +0 '03 O'OO — 0-I3 *'rhis station was established in 1849, to be used in place of the United States Naval Obser\ator>-. where it was foinid both inconvenient and nn.satisfactory to make observations, as it interfered with the regular duties of the obser- vatory staff. It was located east of the Capitol, in an open field, on Fifth street east, near A street north, now covered by buildings. Telegraphic connection with the Naval OUser\'atory lold) was made in 1867: distance V>y wire. 5J5 kilo- meters, or i% statute miles, nearly. ;20 THE EASTERN OBLIQUE ARC. No. 3S. aSeatoTi yWashingtoJx, JD. C, Obs Petershujrg • New Orleo-Tis, Lcl. In order to reach the longitudes of Mont- gomery, Lower Peach Tree, and Mobile, Ala- bama, it was necessary to make a special adjust- ment of certain intermediary longitude stations, which bind them together and connect them with the standard net. They are Petersburg, Virginia, 1S52; Raleigh, North Carolina, 1853; Charleston, South Carolina, 1853; Wilmington, North Caro- lina, 1854 and 1856; Columbia, vSouth Carolina, 1854 and 1856; Macon, Georgia, 1855; Mont- gomery, Alabama, 1856; Lower Peach Tree, Alabama, 1857, ^"<^ Mobile. Alabama, 1857 and 1858.* DiFFERENCK OF i^ongitudf: betwef:n pf.tersburg, VA., AND SEA TON STA TfUN, D. C. Date, 1852. July 7 9 21 22 Aug. 2 7 Number of Diffe rence of stars. loii 111. sit ufle. 15 I 35 •5S3 21 •636 13 ■617 6 and 14 ■559 9 •545 17 •597 — — Mean I 35 '589 ±0 -009 The observer.s were A. D. Bache and G. W. Dean, at Petersburg, and L. F. Pourtales, at Seaton vStation. The observers did not interchange places. Their per- sonal equations were ascertained by direct observations taken at various times. The results, as given here, are corrected accordingly. Giving weights to the individual results in proportion to the number of .stars olxserved each night, we get JA=i'" 35'*-59i±o'-o22o. Petersburg (transit) west of Seaton (tran,sit), i'" 35'^-59i ±tf"022. DIIFEKENCE OF I,ONGITUDE BETWEEN RALEIGH. N. C. AND SEATON STATION, D. C. Date. Number of stars. Difference of longitude. IS53- ;//. 5. \pr. 21 5 6 32742 26 23 ■992 28 23 •S94 30 16 ■987 Mean 6 32 -904: Weightec 1 mean 6 32-87.: rO '044 The observers were B. A. Gould at Raleigh and * Details at these stations published for the first time. .See also report by Dr. B. A. Gould in Coast Survey Report for I664_ J Appendix No. 12, pp. 115, u6. THE ASTRONOMIC MHASURKS. 321 Iv. F. I'ourtales at Scaloii Station. The personal equation correction was deterniineil from flirecl and indirect comparisons. The results given here are corrected accordingly.* Raleigh (transit) west of Seaton ftransit) 6"' 32"'873z!=o"044. DIKKERKNCK OF LONCHTUUK liKTWKKN CI I A N I.IISTO.X . S. C, AND KALICIGJI, X. C. Date. Nvimbcr (;f stars. DilTerc-iice of longitude-. 1853- Apr. 29 May 6 14 3 15 13 in. s. 5 1 2 '007 •061 ■164 Mean 5 12 -077 -^rO -031 Observers: At Charleston, L. R. Oihhes; at Raleigh, H. .\. Could. The personal equation cor- rection being unknown, the probable error of the result is raised toxo~"i5. Charleston, Gibbes Ob.servatory (transit) west of Raleigh (transit) 5"'i2-- oSir^o'-is. Reduction of Gibbes Observatory to Citadel Square (transit) at Charleston. t ""'396. Charleston, Citadel Square (transit) west of Raleigh (transit) 5'" i r-6S4:irO"i5o. DIHFKRKNCK f)F I.ONGn'lTDF: BKTWKKN llll.MiyCTO.W .N'. C, .\ND I'lyi'l-RSISI RC . V.\ pifTereiice Diffi-rciice of longitude referrtd of loiijjitiidc. to D-t and I'.; and means. i: '213 2 \\ 244 Date. N 11 in her 01 servers al- _ ' stars. Wilmington. I'etersbniK 1854. May 8 4 G W. Dean. B. A. Gould. 27 " 1 0. A. W. Dean. D. Bache. |... F. Hourtales. June 5 24 C", W. Dean. I, F. Pourtales. 14 •^ 1 27 L. F. Pourtales. G. W. Dean. ■239 ■239 ■451 •4S0 ■449 ■399 ■219 ■9(2 u-2,M 239 J 2 1 1 '445 2 1 1 -540 Wilmington (transit) west of Petersburg (transit),;^ 2'" 1 i'"340ii=o*"o33. diffkrkncf; of uingitude bf;twef;n colimkia. s. c . -\nd kaleich. n. c. Mean J A Date. Number observers a t— of .stars. Colinnhia. 1S54. Jan 21 Feb. 5 23 14 1 J B. A. Gould. G. W Dean 21 2.^ 1 G. W. Dean. B. A. Gould Mar. 12 10 1 Kaleigli. Difference of longitude. 9 3,=; 821 V 36 '064 j 9 35-7S7 1 3.S-779I 9 35 "942 I9 35 562 ± OS 041 9 35 '9^3 Columbia (transit) west of Raleigh (transit) J 9'" 35''\S62=to''-04i. * F'or further remarks on the methods used at this and some other stations representing the stage of the develop- ment of telegraphic longitude determinations, see Coast Survey Report for 1S53. pp. 56-57. .\ part of the work done at Raleigh is used as an example of a method for determining differences of longitude, in Vol. 1 of Chauvenefs Spherical and Practical Astronomy, 5th edition, 1SS7. t'riie observation for difference of longitude of Charleston, South Carolina, and Sealon Station. District of Columbia, in February, 1S50, was experimental in character, and too weak for use here. ID. for Dean an rt o-"05i. DIFFHRKN'CF: of LONGITUUK KK'rWKF;X CCIJ'MJI/A. S. C. AND I!'lLML\'GTO.V. N. C. Mean J A. Nvnnber of stars. ( )bservers at — Columbia. Wilniiuifton. Difference ut longitude. C. W. Dean. K. Goodfellow. 12 21 74^ ■744 •878 ■6S0 I 12 21740 I ,_, ■660 I 12 21762 12 21 731+0028 K. Goodfellow. G. W. Dean. 1 '' ' '"' I '- 21700 Coluinl)ia ( tran.sit ) we.st of Wilniiiixton (transits 12'" 2l'"73l =bo*'o2.S. DIFFKRKNCK OF l^oNGITfUF, BF:T\VEF.N A/iKVTGOM/-:/^ i'. AIbservers at- 23 30 Montttomerv. (i. W. Dean. F". Goodfellow. E. Goodfellow. G. W, Dean. Difference of longitude, III . i. 110 41 568 1 ■501 I ■S69 I •488 J 110 41 727 J ■595 I 595 I ■520 ) Mean A A. 10 41 '609 10 41 -570 + 015 MonlKOinery (transit) -west of Macon (transit), 10'" 4l'''570 dzC-ois. DIHFEKENCE OF [.oNGITtTDK HFTWEEN LOll'/Ck PI-.ACH TREE. Al.A., AND MO.WGOM ER V. .\\A. Date. Apr. 2 6 7 10 19 20 23 28 Ol)servers at — l,ower Peach Tree. Montgomery 31 14 13 3' 26 18 (',. \V. Dean. E, Goodfellow. E. Goodfellow. G. W. Dean. Difference of longitude. 4 5^ '79-^ ■7-'3 ■736 ■943 4 58790 79.=; ■752 ■774 Mean J A. 4 5S -Soo 4 5877S III. i. 4 5S-789io-oi6 Lower Peach Tree (transit) west >.>{ Montgomery (transit), 4'" sS^'ySQ io^-oi6. THE ASTRONOMIC MEASURES. 32: DiKFKRKNCK OH r/)Nr,rrfi)i<; hi<'.twi<:kn lyroiuij-:^ ai.a , and i.invi:K I'Eacii irei-: .\\.\ Dat c. Nunil of sta ler rs. Mobile-. 'S57- May 21 34 24 25 3S 22 C. W Dean. 26 34 June 2 41 6 1 1 Iv Cioodlellow 7 3^ ohservtrs al — Uiffcrencc of I«. I s. D. and M. 07 '074 s 07 147 3:0 *o \ ^ 07 '396 E. Cioodfellow j ■230 s o7-256_ I •141 New Orleans, Basin street, west of Mobile (transit), 8'" 07"i47iho"'022. Reduction to station Lafayette Square — o '866. AX New Orleans, Lafayette vSquare, anil Mobile S 06 '281:110 '022. Adjustuiciit of S((0)idarv tclcorapliic lonoitiidc sta/ioiis to tlic sttx)idard tcUffraphic longitndt net of tlic rnitcd Slates. Referring to the preceding- diagram , wliich shows the connection of the longitude sta- tions between Washington and New Orleans, it is seen that the three circuits de nand as man}- conditions to be satisfied. The conditional or observation equations are established as foUowsf: AX New Orleans and Mobile A\ Mobile and Lower Peach Tree AX Lower Peach Tree and Montgomery A\ Montgomery and Macon AX Macon and Columbia AX Colnniliia and Raleigh AX Raleigh and vSeatou AX Seaton and Washington (Old Naval Observatory) m. 8 J.l 06 '281 Corrections. * (1) I P 5 I 59 768 (2) 3 4 5'^ -7X9 (3) 3 10 41 •57'i (4) 2 10 22 -250 i5) 26 9 35 •-'^62 (6) >7 6 3-' -^7:. (7) '9 -0 1 2 634 iS) -' -2 52 04 759 *■ Y>. stands for ('.. W. Dean anil M, for A. T. Mosnian. t'rhe nnnibers in coUnnn . eiinal ioihx-> times the sijuare of prolxible errvir. ,24 THE EASTERN OBLIQUE ARC. True value iu standard system 52'" 04''6io, hence the first observation equation: o=+o-i49+(i)^(2) + (3) + (4) + (5) + (6) + (7)-(S) J A Columbia and Wilmington JA Wilmington and Petersburg JX Petersburg and Seaton JA Raleigh and Seaton //A Columbia and Raleigh hence the second equation: 12 21 731 (9) 8 2 1 1 -340 (10) II I 35 -591 (II) 5 16 oS -662 >n. .'^. 6 32 -873 (7) 19 9 35 -862 (6) 17 16 oS 735 o=+o-o73+(6) + (7)-(9)-(io)-(ii) JA Charleston and Raleigh JA Raleigh and Seaton J A vSeaton and Washington (Old Naval Observatory) 5 11-684 (12) 225 6 32-873 (7) 19 -0 12 -634 (8) 2 3 II 31-923 True J/A. in standard s^^stem 11" 3i''923, hence third equation o=o^-ooo— (12) — (7) + (8) Normal equations. Correlate equal 'ens. Corr. I 7 c, c. c. (I) 5 +1 (2) 3 +1 (3) 3 +1 (4) 2 +1 (5) (6) 26 + 1. . . 17 +1 + 1 (7) 19 +1 + 1 — I (8) 2 — I + 1 (9) s — I (10) (II) 1 1 . . — I . . 5 — I (12) 225 — I 0=4-0 •149 +77C,+36C. -21C3 o=+o ■073 +36C,+6oC. -19C3 0^ •000 — 21C1 -I9C. + 246C3 Cx = - -o-ooi 93 c.=- -Q-OOO 11 C3=- -0 -QOO 17 5. 5. (I)=- -0 -0096 (7) = = -0-0355 (2) - -0 -0058 (8) 4-0 -0035 (3) - -0 -0058 (9) 4-0 -0009 (4) - -0 -0039 (10) +0 -0012 (5) - -0 -0502 (II) 4-0-0006 (6) - -0 -0347 (12) +0 -0383 /. IH. i. 5 oX '2-153 1 2 -6375 77 tJ3 "2 -295 5 07 59 '5155 76 59 52 73^ + I 35 -59'^ 5 f^ 35 'K'?' 77 23 46 -Sot 4- 2 II -3412 5 II 46 -4483 77 56 36 724 + 12 217319 5 24 C)S •i8<)2 Si 02 02 703 THK y\STRONOMIC MEASURES. 325 kesultinfT longitudes. A Washiiifi^ton, Old Naval ( Jhservalory Dome AX Washinj^toii and Seatoii \ Seatoii ( transit ) A\ Seaton and I'L-tersbur}^ A Petersburg (transit ) AX Petersburg and Wihniugton A Wilmington (transit) AX Wilmington and Columbia A Columbia (transit ) Check: AX Seaton and Raleigh + 6 32 '8375 A Raleigh (transit ) 5 14 323530 78 38 05-295 AX Raleigh and Columbia -f 9 35 ''''273 \ Columbia (transit ) 5 24 08 ■1S03 81 02 02704 Further — JA Columbia and Macon -)-io 22 '1998 A Macon (transit) 5 34 30-3801 83 37 35 •7or AX Macon and Montgomery -(-10 41 -5661 A Montgomery (transit) 5 45 11 -9462 86 17 59-193 AX Montgomery and Lower Peach Tree + 4 58 '7832 A Lower Peach Tree ( transit ) 5 50 1(1-7294 87 32 40-941 AX Lower Peach Tree and Mobile -\- i 59 -7622 A Mobile (transit) 5 52 10-4916 88 02 37-374 AX Mobile and New Orleans, Lafayette Square -)- 8 1)6-2714 A New Orleans, Lafayette Square 6 00 16-7630 90 04 11 -445 If the above results are compared with those obtained in tlie prehnhnar_\- adjust- ment of the telegraphic longtitnde system as it stood in 1884,-'- it will be .seen that the present longittides are al)out one-tenth of a second of time greater than those fottnd in 1884. This is mainly dtte to the introduction into the system of tlie fourth cable line across the Atlantic Ocean in 1892. The probable errors given in the stunmar}- of restilts are close approximations. * Report of 1884, Appendix No. 11, pp. 407-430; and Report for 1S97, .\ppeiidix No. 2, pp. 197-261. 320 THE EASTERN OBLIQUE ARC. 4. SUMMARY OF RESULTS FOR LONGITUDE. No. 10 II 13 14 ]6 17 Calais Bangor, Thomas Hill Cambridge, Harvard Observatory Cape May Dover Washington, Seaton Station Washington, Coast and Geodetic Survey Office Washington, Naval Observatory (old) Washington, Naval Observatory (new) Petersburg, Roslyn Station Wilmington, De Rosset Station Strasburg Charlottesville Raleigh, vState House Grounds ' Charleston, Citadel Square Statesville, near Simenton College Columbia, Capitol Square Macon, Academy Square Atlanta Montgomery, Capitol Hill Lower Peach Tree, Wilson County Mobile, Public Square New Orleans, 1895, Ii with the arc of the parallel in latitude 39. All necessary details in regard to the observations at these stations are given in the ])ublished di.scu.s- sion of that arc. vSome of the particulars are repul^li.shed in this discussion in the proper place. The various methods employed by the Coast and Geodetic vSurve\' for the determi- nation of azimuths, together with the required formuke and their numerical application, are .so fully set forth in Appendix No. 14, Coast and Geodetic Survey Report for 1880, pp. 261-286, and in a later edition, Appendix No. 7, Coa.st and Geodetic Survey Report for 1897-98, pp. 377-407, that no further reference is required. It will suffice for a full exhibit of the azinuithal results to present for each station the following par- ticulars — the method employed, instrument u.sed, stars observed, the arrangement and composition of sets of observations, the number of measures and position of circle or instrument, and any other details pertaining to the operation; the names of the observers, and, finally, the individual results in the form of an abstract, together with their prob- able errors. The apparent places of stars are taken directly from the American Ephemeris or derived from Gould's "Standard Places of Fundamental Stars," Washington, 1S66 (.second edition), except in a very few cases. The probable error of the result of a .single .set and that for the resulting azimuth of the mark are due to ob.serving errors and exclude the probable error in the star's catalogue place. When referring the azimuth of the mark to the triangulation, the probable error of the referring angle is not given, as in general it is not accurately determinable. The local adjustment of the horizontal directions at a station include that of the mark, and the angle between the mark and the direction of a line in the triangulation was corrected l)y applying to it the iincni shift or average correction to all the directions at the .station in the .second or figure adjustment. The j^robable error of any resulting azinuith of a line in the triangulation may l)e estimated as not less than one-half of a second. One-third of a second lias l)een taken for the probable error of an observed direction, resulting from the figure adju.stment, whence dto""47 for the angle "mark and line." Coml)ining this with ±o"'25 as the proliable error of the mea.sure of the azinuith of the mark, we get ±o"'53 for an approximation oi the probable error of a resulting azinuith of a line. For ordinary or le.^^s preci.se work this value may rise to three-fourths of a second. 327 328 THE EASTERN OBIJOUE ARC. (p = 44 59 2. I. COOPER, Maine:. A = 67° 2S''i west of Greenwich. The 75'"' direction theodolite No. i (Troughton & Simms) was mounted over the triangulation .station. Focal length of telescope, 115 centimeters; clear aperture, 7'5 centimeters. The azimuth mark was located upon a hill to the north of the station and distant about 2 miles. Light was shown through an aperture three-fourths of an inch in diameter; for day observations a wand i foot in length and i inch in breadth was placed above the center of the aperture. A set of observations on Polaris generally consisted of 3 observations of the mark, telescope direct, and 3 observations telescope reversed, followed by 5 observations of the star, with the necessary time and level record; the instrument was then reversed and the observations were repeated in the reverse order. In ca.se of A Ursae Minoris 6 observations were made upon the star both before and after reversal. One division of level = i"'43. Ob.servers, G. W. Dean and R. E. Halter. Probable error of a .single result for azimuth ± o"'Scj. Siinimary of 7'esults for aziuinth al Cooper, Maine. Date. 1859. Polaris near eastern elongation Position. ,Mark^ ^ A frsa; Date. I^i9- Minoris near Position. upper culmination. Mark . W. of N. ^ C ' " " Sept. 9 IV 2 49 47-53 +0 -85 Sept. 9 \\ 2 49 47 '49 + 1 -50 12 V 48 -06 +0-32 12 \ 47 '94 + 1 -OS 14 I 50 -07 -1-69 14 I 49-09 ~o -10 15 II 46-58 + 1 -80 15 II 50 -69 — I -70 16 III 47 -So +0-58 16 III 47 '93 + 1 -06 iS III 49-08 — 0-70 18 IV 50 -82 -I 83 19 V 49 '56 -I -18 •31 Mean 2 49 48-99 + Mean 2 49 4S-3S + 1. ■40 / // Mean of groups Diurnal aberration 2 49 48 -68 -0-31 Azimuth of Mark 17 7 10 n -63 -_ho"-25 Angle between Mark \\\A Howard IS 5 16 59 'SS Azimuth of Howard 35 t 53 12 '05 2. HOWARD , MAINK. (p = 44°37'-8 \ = 67=23' -S Theodolite No. i was mounted over the station. The mark was located upon a hill about I Yz miles north of the station. Light was shown through an aperture three-fourths of an inch in diameter; a wand i foot high and i inch wide was placed above the aperture to ser\'e as day mark. In the case of Polaris a set of observations consisted of 3 pointings on the mark with telescope direct, 3 pointings on the mark with telescope reversed, followed by 5 pointings on the star, or 6 in case of S ITrsae Minoris, with the necessary level and time records; the instrument was then reversed and the above obsei^'ations were repeated in the reverse order. One division of level =i"'43. Observers, G. W. Dean and R. E. Halter. Probable error of a single result for azimuth rbo"'8o. THE ASTRONOMIC MEASURES. 329 Sininiiaiy of results for azimullt at Harvard . Maine. S Ursx' Minoris iieai- iij>i)ir ciilmiiKitioii. ['rs;c Minoris near eastern elongation. Date. rosition. K. of N. '859- , ,, July iS I 7 ¥> <>i 72 21 n \"^ M 23 in 05 '05 24 IV 0472 25 29 II 02 ■.« 05 'IJ Mean Diurnal aberration 7 •1i'> 04 -39 ±0-35 +0-33 J Date. 1859. I'osition. Mark K.of N. 1 " d -0 '33 July IX I '. 46 03 35 4-0-4I 20 II 05 49 -'•73 ■-o-6f! 21 11 05 '63 1S7 -"■33 23 III 04 -.so -074 + 2 '06 24 IV 03'I7 +059 -074 25 V 03 46 +030 28 V 03 43 +0-33 29 I 01 72 f2-04 Aug. 6 IV 02-84 +092 M S ^-an III 04 00 -024 7 46 0376 iO •25 Dinrna aberration ^031 Mean of j^roups Azirutth of Mark Angle between Mark ami Pigeon Azimuth of Piycoii 7 46 04 •40 1S7 46 04 ■40rtzo" -27 123 51 19 29 63 54 45 • " 3. HUMPK.\CK, M.VIXK. (p = 44° 5i'-.S A = 6S°o6'-6. Theodolite No. i was mounted over the trigonometric s'ation. The mark wa.s located in an open field estimated to be about 2 miles from the station, light was shown through an aperture three-fourths of an inch in diameter, and for day observations a wand I foot high and i inch wide was placed vertically above it. A set of observations consisted of 3 pointings on the mark, telescope direct, and 3 jiointings telescope reversed, 5 pointings on the star for a Ursae Minoris and 6 for S Ursie Minoris. The instru- ment was then reversed and the observations were repeated in the re\-erstj order; the necessary time and level records were made for ])oth positions t)f the instrument. One division of level = i"'43. Ob.server, G. \V. Dean. Prol)able error of a .single result for azimuth zfc o"'86. Suiinitary (f results for a::iiiiiit/i at Iliinipback, Maine. S Ursse Minori.s near upper culmination. aUrsx Minoris near eastern elongation. Date. Position. Mark K. of N. A Date. Position Mark E. of N. A 1858. ' t> 185S. ' r/ ,, Aug. 9 Ill 114 20 12 '86 -0 07 Aug. 9 III 14 20 13 11 - 1 01 13 IV '-■•39 +0 40 12 III 1 1 -37 + 073 14 \' 12-51 +0 28 13 IV 11 -00 + 1 10 16 I 11-52 + 1 27 14 V 10-71 •1- ' 39 17 II 14 -68 — 1 35 89 16 17 19 20 23 2.S I II II IV V I 1 1 -63 '3-65 14-17 10-84 11-13 '3 '34 -fo-47 -2-07 + 1-26 +0-07 -1-24 Mean 114 20 12-79 -*^0' Mean 14 20 1210 ±0 2S Diurn al aberratio u +0-33 Diurna aberration +0 -31 ' / Mean of groups 114 20 12 76 AzinuUh of Mark 294 20 12 •76r £:0"-22 Anglo between Mark a IK C ooper 39 37 40 "40 Azimuth of Cooper 254 42 52 36 * Reji-oleii bv ivirce"s criterion. 330 THE EASTERN OBLIQUE ARC. 4. MOUNT DESERT, MAINE. (?>=44° 2i'-i. /l=6S° i3'-6. Theodolite No. i was mounted over the triangulation station. The mark was estabHshed near Hulls Cove, and is distant from the station about 4 miles. Light was shown through an aperture one inch in diameter, and above this a wand was adjusted verticalh' for day observations. A set of observations con.sisted of 3 pointings on the mark, telescope direct, 3 pointings telescope reversed, 5 pointings on a UrscC Minoris or 6 on A Ursse Minoris. The instrument was then reversed and the observations were repeated in reverse order; time and level records were made for both positions. One division of level i"'53. Observers, A. D. Bache and G. W. Dean. Probable error of a single result for azinuith zh o"'So. Siiiiiiiiary 0/ irsii/ls for aziiiut/h at i\foHnt Desert, Maine. a UrsiL Minfjvis, 1 it-ar eastern el< )n nation. A llrs;e Minoris, near upper culmination Date. PoMtioii. Mark W. of N. J Da te. Position. Mark W. of N. A 1S56. C ' " ,, 1856. / // ft Aug. 30 II 12 19 oS "89 4-0 -66 Sept I II 12 19 II -08 — I 04 Sept. I II og '20 -f 0'3.S 2 III 07 '65 -f^-39 2 III 09-24 + 0-31 3 IV 10 -88 -0-S4 3 III 07-63 + 1-92 4 V 10 -61 -0-57 4 IV 09-S9 --0'34 7 I 08-78 + 1 -26 5 v 11 -09 - ' '54 18 III II -26 — I -22 7 I OS -77 -fo-7S 9 I 10 -S6 -1-31 16 IV 09 -79 -0-24 17 v Mean 10-10 to -22 Mean 12 ]q og -55 _ 12 19 10 04 + ■41 Mean of groups 12 19 0979 Diurnal aberration -- o'3i Azimuth of Mark 167 40 50-52±o"-2o Angle between Mark and Ragged Mountain S9 10 03 -95 Azinuith of Ragged iNIountain 7S 30 46 "57 5. MOUNT HARRIS, M.\INK. V = 44° 39' 'g- ^ = 69° o8'-9. Theodolite No. i was mounted over the triangulation .station. The mark was located upon the south side of the old stage road from Dixmont to Hampden, about 2^ miles from Dixmont village; light was shown through an aperture i inch in diameter, and for day observations a wand i foot high and i inch wide was placed over it; the lower half of this wand was covered with black cotton cloth and the upper half with white cotton cloth. A set of ob-servations con.si.sted of 3 pointings on the mark, telescope direct, 3 pointings telescope reversed, 5 pointings on the star if a Ursae Minoris or 6 if A Ursse Minoris. The instriunent was then reversed and the observations were repeated in the reverse order; time and level records were made for both positions. One division of level = i"'54- Observers, A. D. Bache and G. W. Dean. Probable error of a single re.sult for azimuth ± o"'98. THK ASTRONOMIC MEASURES. 331 Siiiiiiiiary of rcsu/ls fur a-:iinii//i al J/uiiii/ If arris, Maine. atlrsic Minori.s near eastern cloiiji: li( jii A I rsie Miiioris ne ar upper culmination. Date. I'o.sitioii. Mark K. of N. J Date. ro.sition. Mark K. of N. A 1855- / " /' 'S.55 / " " Aug. i9 V 62 37 2y32 1 I -03 Aug. 30 V 62 37 30 -y* 4-1-08 y> V 29-19 t-I -16 Sept. 4 !V 32 -ss -I 19 Sept. 3 IV 3" '25 1 OK) 5 in 30-68 +0-98 ^ IV 30 '97 - 62 6 n 32 93 -1-27 5 III (26-22]* 8 I 31 -28 +0-38 6 III 29-68 fo-67 S II 29 -es 1-0 -67 10 I :,o -90 0-5.5 II I 3? '47 -3-12 12 II 31 -4S -I-I3 14 III Mean 28-62 ■3" + 1 -73 Mean (■'^ 37 3"'35±o 62 37 31 -66±o 35 Mfiiii by groups Diurnal aberration A/.iinnth of Mark Angle between mark and Hiinijiback A/.inuith 4 III 49 '93 -0-45 14 III 50-46 - 1 '03 14 IV 48 -82 +0-66 IS IV Mean 50-21 -0-78 y -27 15 V Mean .,S-26 + 1-22 10 49'43± 10 49 '4Si:0' -24 / ff Mean of groups 10 49-45 Diurnal aberration -0 •51 " Azimuth of INIark 179 49 10 •86±o'i7 Angle between Mark and Agamenticus 207 06 37 74 Azimi th of Agamenti CllS 26 55 48 ■60 334 THE EASTERN OBLIQUE ARC. lO. MOUNT PLP:aSANT, MAINE. ^ <^=44° oi'-6. A = 70° 49' -4. Theodolite No. i was mounted over the triangulation station. The mark was placed nearly in line with Mount Blue, on the summit of the next ridge and about i mile dis- tant from the station. The angle between the mark and Mount Blue was measured micrometrically with the eye-piece micrometer of the theodolite. The angle of depres- sion of the wand placed over the mark was 2^°. A set of observations consisted of 3 pointings on the mark with telescope direct, 3 pointings on same, telescope re\-ersed, 5 observations of the star with time and level record; the instrument was then reversed and similar observations were made with their order rever.sed. One division of level = o"-97. Observers: A. D. Bache, C. O. Boutelle, and W. P. Trowbridge, U. S. E. Probable error of a single result for azimuth ±0" '90. SiniiJiiary of resnlls for aziunith at ISFount Pleasant, Maini a Ursje Minoris near lower culmination. Date. 185 1. July 22 Aug. 3 8 14 Mark E. of N. 25 59 i'^' '30 19-17 1777 21 '00 +0-76 —0 'ii + 1 '29 -I -94 a Urste Minoris near upper culmination. July Aus;. I'osition, \' V III Mark E. of N. 25 59 17 '6,^ 20 '64 I9'fil + 1-66 -I '35 -o'32 25 59 19 ■o6±o"'4S 25 59 19 '29*0" '60 Mean of groups Diurnal abberration Azimuth of Mark Angle between Mark and Mount Blue Azimuth of Mount Blue 25 59 19-16. +0 •31. 205 .59 19 '47^0'' -34. 02 '09. 2"5 59 2' '56. II. AG.AMENTICliS, MAINE. UHlli al /\i^aiiii)ili( us, iMaiiw. a Ursie Miiioris iif.'ir cislcrii eloiiHalioii. a (rsu; Miiiori- near western eloiijialioii. Date I'ositioii. Mark I'., of N. A Date. I'« ^itioii Mark K. of N. J 1S47. Sept. 17 IV 114 OS 59 '.S? -1 iri 1847. Sept. 2i IV t I 4 (>'5 60 -64 -'"75 22 \' 60-57 -2 -16 22 \- 58-12 +0-77 Oct. 4 I 57 '92 + 0-49 (Jet. 5 1 59 •'*3 -0-94 14 II 5S'3i + 0'I0 15 II 58-18 +0-71 i6 III Mean 55 -feS + 2-7,5 56 17 M III ean 57-6*4 114 OS sS-89±o" + 1 -21 1 14 oS 58 ■41+0" •38 / // Mean of groups I 14 08 5S •65 Diurnal aberration \ •31 " Azimuth of Mark 294 oS 58-96-0-32 Allele between Mark and Thon pson 291 32 "3 ■45 A/.iniuth of Thompson 2 36 53 •51 12. CUINSTOCK, NI'-.W H.\MI'.SHIKI-;. near eastern eloni. ation. 5 rrs .e Minoris near ni>i>er enhnination Date. I'ositio.i. w'^'of N. Zl Date. Position. Mark W. of N. J . 1S60. C ' " " 1S60. ' " >• July 24 II 40 29 49-54 +0-36 July 24* II 40 29 51 -40 -'•53 25 III 50-66 — 0-76 2S* III 52-90 -3 03 27 III 4S-23 + 1-67 27 III 49 01 +0-S6 28 IV 49-06 +0-S4 2S IV 4S 63 r + 1-24 30 I 49 -6S + 0-22 ,30 I 48 -80 + 1-07 M II 50-50 -o-6o 31 II 50 03 --0-16 Auk. 1 \- 49-94 — "04 .\un. 1 \- 48 - 1 2 + 1 -75 2 IV 51 -3"^ -1-4S 2 V 49 4^ +0 39 3 I .so- 10 -0-20 0" -21 3 Men 1 n 50-48 -0-61 Mean 40 -'u 49-901 40 2i) 49 S7±o' '34 Diurua 1 aherr;\tiou o-_^i Din nal al>t rrati on -0-33 Mean of group.s 40 / 29 49 '37 " Azimuth of Mark '39 3^' 10-43 -o-iS Angl ebe twecn Mark ami Mount rleasant 7>^ 13 23 17 Aziti uth of Mount Pleasant 217 43 33 ^^^ ►The results for July 24 :uul 25 are from ohserv.Uions of 24 l'rs;e Minoris and of 6 l"rs;c Minoris, < 336 THE EASTERN OBLIQUE ARC. 13. UNKONOONUC, NEW HAMPSHIRE. 3 Mean of (^ and A Urste Minoris at upper transit Mean of 5 1 Cephei at lower transit Mean Diurnal aberration 7-65 8 -02 7-84 — o '3 1 Azimuth of Mark Angle between Mark and Blue Hill Azimuth of Blue Hill Difference of azimuths, transit and dome Azimuth center of dome to Blue Hill 179 59 52-47±o-i3 176 23 05 -48 356 22 57 -95 + 2 28-42 356 25 26 -4 ♦Rejected. _. THE ASTRONOMIC MEASURES. 339 17. H1.UH HII,I„ MAS.SACIllSKTTS. (^ = 42" 12' A = 7i'^ 06' '9. Theodolite No. i was niounled over tlie triangulatiou station. A set of observations consisted of 3 pointings on the mark,* telescope direct, 3 pointings on .same, telescope reversed, and 5 pointings on the .star, with time and level records. The instrument was tlien reversed and the preceding operations repeated in the reverse order. The instrument was kept leveled. Chief of party, A. D. Bache. Probable error of a single result for azimuth d=o"'89. Suiiunary of rciulls for aziinutli at ISliic Hill, Alassacliusciis. a Ursie Minoris near western elongation. o frscK Minoris near eastern elongation. Date. Position. Mark K. of N J D.ite. I'osition. Mark E. of N. J 1845.. ' 'f ,, 1^45. 1 ,1 Sept. 24 Ill 2 02 33 7S -0'42 Sept. 25 Ill 2 02 30-25 + 262 27 IV 33 75 -o'.^9 26 IV 33 -z" —0-41 Oct. I rt VI 34 '49 -■■'3 27 IV 33 '9' -1-04 2 I 34 '59 -1-23 2S II 33 '29 -0-42 3 11 30-99 + 2 '37 29 V 33 '32 -0-45 13 v 32 '57 -1-0 79 Oct. I VI 3' '94 +0-93 Mean •.3S 2 I Mean 34 '07 o"-3 -I -20 2 02 33 '36 ±0" 2 02 32'S7± » f // Mean of groups 2 02 33"" Diurnal aberration -0-31 // Azimuth of Mark IS2 02 33 '42^0 •25 Angle between Mark and Manoniet '23 54 56 -63 Azimuth of Manomet 305 57 30-05 18. SHOOTFI.YING, MASS.\CHfSETTS. '4' .S2 '0,; 5274 .S3 '20 54 '26 53 '05 5" '95 52 '29 .) .12 52 -62 J + 1 '21 +0'59 — 0'12 -o-.sS -I ■64 -0-43 +0-67 + o'.33 ■21 Sept. 26 27 29 Oct. I III IV v v v V 4 42 56 'Rl 55 '19 56 55 52-86 55 "04 53 -S? — I ■7^ -013 -I 49 -h2-20 4-1 IQ 4 42 55 '06+0" -42 Mean of groups Diurnal aberration Azimuth of Mark Angle between INIark and Rlue Hill Azimuth of Blue Hill 4 42 53 "84 — o -3 1 // 175 17 "6-5 rbo-3i O ■QC) 175 17 (16 -5 2 1. KKACONPOI-K, RHODK ISI-.VNI),

=4o°4S'-S. A = 73° 25'-6. Theodolite No. i was mounted nearly over the triangulation station. The azimuth mark was placed near the station Huntington, 4,1 kilometers distant from West Hills station.* A .set of observ^ations consisted of 3 pointings on the mark, telescope direct, 3 pointings on same, telescope reversed, 5 pointings on the star, if Polaris, 6 if fJ Ursae Minoris, with time and level records. The instrument was then reversed and similar observations were made with their order reversed. One divi- sion of level=i"'oo. Observer, G. W. Dean. Probable error of a single result for azimuth zfco"'57. Sumuiary of results for azimuth at West Hitts, Nezv York. a Urs:e Minoris near eastern elongation. 5 Ursie Minoris near upper culmination. Date. Position Mark E. of N. // Date. Positio 1. Mark E. of N. A 1865. ' V ,, 1.865. , ,f ,, Aug. 4 v 2 23 58-23 + 1 -00 Aug. 4 V 2 23 58-63 -Ho -55 8 IV 59 02 +0-21 8 IV 58 '55 + 0-63 9 II 60 -87 — I -64 9 II 58-72 +0-46 II I 58-21 + 1 -02 u I 5876 -(-0-42 12 III 60-61 -1-38 12 III 59 '68 —0-50 15 v 58 46 -1-0 -77 15 IV 60 "oo -0-82 16 II 58-85 +0 -38 16 I 59 '94 -076 18 III n 59 '62 -0-39 ■25 Me m 2 Mea 2 23 59-23 + 0" 23 59-18 + 0" ■I? Diu rnal aberration +0-31 Dm rna I abc rration -t-033 Mean of groups 2 23 // 59 '53 Reduction to station +0 •40 // Azimuth of Mark If- 2 23 59 "93 ±0-15 : Angle between Mark and Wooster 7 26 21 ■61 Azimuth of Wooster 1" 74 57 3«'32 *Tlie geodetic station was found to be 0-47 of an inch SW. of the point at which the azimuth observations were made; the correction to the azimuth when referred to the geodetic station is 40" -40. THE ASTRONOMIC MEASURES. 345 26. BKACON llll.f,, M'.W JKRSKY. ' Urs^e Minoris and ±o""67 for 51 Cephei. Suiiiniaiy of results for a::i)niitli at /Iracoii Hill, Xcw Jersey. 6 UrsiL' Minoris near npper cnlniination. 51 Cuphei iK-ar lower culmination. Date. C ani]). Mark W. of N. J Dale. Clanii). Mark W. of N. A 1875. „ „ i«7.S. „ ., Aug. 19 E 7 '95 -o'S6 Aug. 19 E 7-90 -024 21 W 5 -53 + 1 '56 21 W 6 -07 + 1-59 25 W 8-63 -1-54 25 W S-7S — I 12 26 E 6-II + 0-98 26 E 7 '21 -045 27 W 6 '50 +0 -y) 27 \\ 7 41 + 0-25 2S E 7 '81 -072 28 E s-5g -0'93 Mean Diurnal a berr ■itiou 7 '09 + 0" -0-33 •33 Mean Diurnal a berration 7-66-0" -030 ■27 Mean of groups Azimuth of Mark Aiifilf between Mark and Weasel A/.iinttth of Weasel o 7 '06 •79 59 52 942=0 -21 3 35 36 95 I S3 35 29 "^9 27. Mor.NT KOSK, Ni;\V JICKSKV. pointings on the star, followed by the same operations in the reverse order, with tlie necessary noting of time and level readings; circle used in V positions. Ob.server, R. D. Cntts. Probal^le error of a single result zb I "75. Results for azimuth from observations of a i'rs(r Miiions near eastern eloui^ation, in August and Septemlwr, 1866. o / // Mark west of .south 3 05 07 '20 Diurnal aberration — o -32 Azimuth of Mark 3 05 07 •52^=0''' "40 Angle between Mark ami Turkey Point i 30 24 'oi Azimuth of Turkey Point 1 34 43 51 30. CAPK HENLOPEN LICHT-HOISE, DELAWARE. '27 219 46 57 ••S9 THE ASTRONOMIC MHASlKi:S. 349 Remits for aziniuth from observations of a IJrsec Miiioris near eastern and 'luestcrn elongations and of A (Jrsie Minoris near upper culmination , in Septonljer and October, /8§o. o / // // Mark E. of N., 5 results from '^° 53' ■4- A =77° 00' -o. The 75"" direction theodolite No. i was mounted over the triangulation station, and the mark was on the tower of the Soldiers' Home, about 3/2 miles distant. A single result for azimuth is derived from 34 sets, each set of observations consisting of 8 pointings on the mark and 8 pointings on the .star, one-half with telescope direct and one-half in reversed position. The star was observed alternately direct and reflected in mercury, times noted. The circle was used in \'II po.sitions. Observer, C. O. Boutelle. Probaiile error of a single result ±o"'72. Result for azimutli from observations of a t'rsic Minoris at various hour angles, in December. /S6S. and fanuary, iSb^. o / // Mark west of north 10 01 13 73 Diurnal aberration o "32 /' Azimuth of Mark 169 5S 46 ■59=^:0 mS Angle between ;Mark and Hill 95 34 07-17 Azimuth of Hill 265 32 53 76 17S '9 3,S -22 'fO'32 // 35S 19 3S •54=^0 '29 89 3" 15-08 26S 49 23-46 3" 52 60 •62±o '51 59-29±o-48 59 "955 +0-315 2IO 53 00 -27^=0 '37 O 0[ 41 '5^ 2IO 54 41 -7^ 350 THE EASTERN OBLIQUE ARC. 36. CAl'STEN, DISTRICT OK COLUMBIA. 'P=38°55'-5. A=77°o4'-4. The 75"" direction theodolite No. i was mounted over the triangulation station, and the mark was about a quarter of a mile distant. A single result for azinuith is derived from a set of observations consisting of 6 pointings on the mark, one-half with telescope direct and one-half with telescope reversed, 10 pointings on the star, one-half with tele- scope direct, and one-half, telescope reversed; finally, 6 more pointings on the mark with times noted and levels read. For culminations two sets were taken and coupled, one made before, the other after culmination. Circle used in V positions. Observer, G. W. Dean. Probable error of a single result, star near elongation dLo"'88 and star near culmination =ti"'o8. A'cs/iZ/s /'or aziinutlt from observations of a Urscc Jfinoris near easier)! e/om^a/ion and near Imvcr enhninafion , in May and June, iS^i. o / // // Mark E. of N., 3 observations near eastern elongation Mark E. of N., 5 observations near lower culmination Mean, Mark east of north Diurnal aberration Azimuth of Mark ♦ Angle between Mark and vSoper Azimuth of Soper 37. SUG.\R LOAF, MARYLAND.

=},1° 17' S- A = 79° 05' -2. The 35"" direction theodolite No. lo wa.s mounted over the triangulation station; the mark was on belfry of court-house at Lynchburg, abotit 10 miles distant. Fort>- six sets of observations were made, each set ctinsisting of a pointing on the mark, 2 pointings on the star, one direct, the other reflected in mercury, reversal of in.stntment and series of observations, as before, but in the reverse order, times noted. The circle 21 23 30-34 242 29 57 -Si 263 53 28-15 352 THE EASTERN OBLIQUE ARC. was used in XXIII positions. Observer, A. T. Mosman. Probable error of a set or of a single result ±i"'54. Remit for azifuuth from ohseri^ations of ix Ihscr Minoris at various hour ambles, in November, 1875. o / // Mark west of north 20 48 1 3 ' 1 1 Diurnal aberration — o '32 " Azimuth of Mark 159 u 47 -21^0 -23 Angle between ]Mark and Spear 64 16 54 '53 Azimuth of vSpear 223 28 41 74 42. KI,I,IOTT KNOB, VIRGINIA. (^=38° 10' -o A=79° 18' -9 The 50"' direction theodolite No. 114 was mounted over the triangulation station, and the collimator was mounted on a brick pier 29 feet distant. Thirty sets of observa- tions were made, each set consisting of a pointing on collimator, 2 pointings on the star, one direct, the other reflected in mercury, times noted, reversal of instrument and series of observations, as before, but in the reverse order. The circle was u.sed in X positions. Observer, A. T. Mosman. Probable error of a single re.sult ±i"'50. Result for aziinutli from oliservations of ^x IJrscr iMinoris at I'arious hoiiiauiilcs. in .liiffust. jSyS. o / // Collimator east of north i 41 34 '52 Diurnal aberration ^o '32 " Azimuth of Collimator 181 41 34 •84±n -27 Angle between Collimator and Humpback 121 43 49 '53 Azimuth of Humpback 303 25 24 -37 43. MOORp;, NORTH CAROLINA. ,^3=36° 23'-9. A=8o° i7'-o. The SimmstraiLsit, Coa.st Survey No. 8, was mounted in the meridian of the triangu- lation station, 7 feet to the north. Focal length of telescope i"''io, clear aperture 7'™, magnifying power 45, pivot inequality for clamp west +o"'-o2; resulting value of one division of eyepiece micrometer before November 15, o"'487o and after chang- ing focus to the close of the series o" -4804^0" '0002. Value of one divi.sion of level B = i"ii. In connection with the observations for time, those for azimuth jiroper consist of raicrometric measures between the verticals of the star and mark. The light at the mark was shown through a %-inch aperture; it was distant from the station 5>^ miles and appeared under an angle of depre.s.sion of 2° 25'. A set of observations generally consisted of 7 or 11 transits { times noted by a .sidereal chronometer) of the star over the micrometer thread set in advance to a whole or to half a turn, in.strument clamp west. In connection with the.se, from 5 to 10 point- ings were made on the mark, with clamp east, and the same number with clamp west. The level was recorded with each .set. When measuring the horizontal angle between the mark and the line to Buffalo the transit instrument was used as a collimator. The right ascensions of the stars were taken from the best .sources available. Ob.server, A. T. Mo.sman. Probable error of a single result for azimuth as derived from all the stars ±i"'io. THE ASTRONOMIC MEASURES. 353 Date. 1K76. Sniiniiary 0/ tTsu//s for arjiiiml/i al iS/anyc, Ni»ili Carolina. ITlic tabiilrir rrsuUs iiichKl Star observed near up- ,. , . . ^ per culmination. ' '■^'^'' '•"' '^• tile correction lor cliiiriial aberration.] Star observed near low- Nov. i.S Nov. 21 Nov. 22 Nov. 24 Nov. 26 Dec. Dec. 1 2 Dec. 3 Dec. ,S 1879 T. Y. C. a Urs, Min. I r Cephei 79 Draconis a Urs. Min. /3 Cephei I I Cephei a Urs. Min. Ti Cephei 226 Cephei a Urs. Min. II Cephei 79 Draconis 226 Cephei 79 Draconis II Cephei 79 Draconis V Cephei a Urs. Min. II Cephei 79 Draconis y Draconis 4 163 Groom. a. Urs. Min. 226 Cephei V Cephei 4 163 Groom, a Urs. Min. 23 -96 21-83 22 '90 21 -311 24 •2kJ.22'99 23 tA 25 -o^l 24 ■S9!-24'8o 24-42] 24 -241 24-l6|23-07 20 -Si J 22 81123 -53 22 -63) 26-68 27-821 26 63 f25-20 22 37 23 •97] 25 '15 25 "99 25'17 24-17 2573 24-67 26 -331 22-691 24-24] f24 -24 Date. 1876. er ciilniii Nov. >.S I Draconis 32 Camelo. Nov. 21 I Draconis 32 Camelo. Nov. 22 I Draconis g Draconis 32 Camelo. Nov. 24 1 Draconis 9 Draconis Nov. 26 I Draconis 9 Draconis A Draconis Dec. I 9 Draconis Dec. 2 9 Draconis A Draconis 4 Draconis K Draconis 32 Camelo. Dec. 3 32 Urs. Maj 9 Draconis 4 Draconis K Draconis 32 Camelo. Dec. 5 9 Draconis K Draconis 32 Camelo. .Mark K.of N. 2.5 -691 19 "63J 24-84 26'io 22-66 25 '47 21 -21I 21 ■9i>2o-89 19-56J 23 30 22 -46 22 -8S 23 -22j 22-63|23-2I 23 -A 23 15 21 -37 22-76 22-71 20-99 ■9 yi, 22-54 22 -.'^5 20 92 20 92 >9"39 23 -201 21 •43>22-19 21-94) 21-44 21 -26 Dail}' mean values of mark R. of N. from .stars at upper and at lower culminations: Nov. 15 22 -78=^0 -55 21 24-23 0-50 22 22-85 045 24 22 -9S 0-50 26 23 37 0-45 Dec. I 24-91 -78 2 23 '32 0-37 3 23 -20 0-34 5 23 21 0-42 Weighted mean 23 -301^0 -15 Azimuth of Mark Angle between Mark and Buffak-) Azinuith of Buffaki 4192 — No. 7 — 02 23 iSo 00 23 -30=1=0 -15 21 26 52 -1 1 •5S 33 3' 19 354 THE EASTERN OBLIQUE ARC. 44. VOUNG, NORTH CAROLINA. II 36 42 J VIII 35-39 ) Oct. 29 III 39 93 Nov. 13 IX 32 50 1 III 38-32 39-72 I.\ 33-15 [ 32-89 HI 40-90 I.\ 33 02 J IV 36 -74 X 40-28 1 IV 35-76 36-12 X 37-01 \ 37 -87 IV 35-85 . X 36-3- I Oct. 30 v 37-42 Nov. 14 XI 35-77 1 V 37 -'4 ■ 37-96 Nov. 15 XI 35-51 [ 36 06 VI VI 39-3' 38-37] 38 -45 I 37 -Si XI Mean .;-s., 1 36 20 37 41 ±0" -4 VI 36-62 ) Mean, Mark east of north Diurnal aberration Azimuth of INI ark Angle between Mark and Rabun Azimuth of Rabun 36 20 37-41 -fo-3i " 2X6 20 37 -72^=0 -42 331 49 50-17 iSS 10 27 -89 358 THE EASTERN OBLIQUE ARC 48. SAWNP;E, GEORGIA. : 34° 14' -I. A = 84° 09' 7. The 75"" direction theodolite No. i was mounted over the triangulation station. The azimuth mark was placed on a hill north of the village of Ciimming, 2*7 miles dis- tant from Sawnee; light was shown through a half-inch opening and appeared under an angle of depression of 2° 38' '7. A set of observations consisted of a pointing on the mark with telescope direct, 2 observations of the star, one of image direct, the other of image reflected in mercurj- with time record. The instrument was then reversed and the preceding observations were repeated but in the reverse order. Observer, C. O. Boutelle. Probable error of a single result for azimuth zti""50. Siiiiniiajy of results for azimuih at Sanmee, Georgia. a UrscC Minoris at varions hour angles. a Ur.'«e Minoris at various hour angles. Date. Position. Mark E. of N. Mean by positions. Date. Position. Mark E. of N. Mean by positions. 1873- / " ,, 1873- / '/ " Oct. 13 IV 139 25 19 01 Oct. 17 I 139 25 17 '96 IV 21-17 I 21-95 IV 19 67 19-18 I 18-66 20 -86 IV 17 90 I 21 -28 IV 18-15 Oct. 21 I 24-47 Oct. 14 V 17 '2.5 II 16-05 V 21 -62 II 18-75 V 22 -oS 19.84 II 14-71 16-67 Oct. 15 V 16-07 II 16 -60 ^ V 22-17 II 17-24 , VI '9 95 Oct. 22 III 16 -90 VI 19-98 III 16-66 VI 18-31 19 -05 III 16-01 17-16 VI 17-62 III 19-12 VI VII 19-38 20 -64 III Mean 17-13 Oct. 16 139 25 19-06 + 0" "41 VII 21 -18 VII 20-90 20 -68 VII 21 00 VII 19-69 Mean, Mark east of north Diurnal aberration Azimuth of Mark Angle bet-ween Mark and Currahee Azimuth of Currahee 139 25 19 '06 +0-31 " 3'9 25 i9-37±o-4i 286 09 06-75 245 34 26-12 i THE ASTRONOMIC MEASURES. 359 49. ATLANTA MIDDM-. HASK, CHORCIA. 'fi=?,3° 54' -3 A=84° 16' "6. The 75"" theodolite No. i was mounted over tlie trian^ulation station. Tlie a/.i- mutli mark was located at the north end of the base, 3 miles distant from Middle Ha.se; li^ht was shown throitj^h a half inch aperture.* A set of observations consisted of a pointing on tlie mark with telescope direct, 2 observations of the star, one observation with star direct, the other with image reflected in mercury, with time record. Tlie instru- ment was then reversed and the preceding operations were rejjeated, l)ut in the reverse order. Observer, C. O. Boutelle. Probable error of a single result for azimuth ±i"'6i. Suiniiiarv of results for aziuiiilli at .Itlaiita .^fiddle Base, Georgia. I'rsiL' Minoris ;\t various hour anglts, <• IrsiL Minoris at various hour angles. 1873- Jan, 1 Jan. Jan. 14 Jan. 21 Jan. 23 ition. Mark K. of N. ' " I 52 08 03-16 I 04 '02 I 06-30 I 05 '37 I 04 '93 J II 06-33 II 03 '35 II 04-92 II 03-90 II 03-70 III 07-82 III 08-99 III 10-47 III 09-26 III II '23 J IV 10 -01 IV 08 -75 IV 09-82 IV 09-96 IV 07 '37 J 09-13 Mean by position. Dat f. Position. Mark E.of N. " >873- Jan. 24 v 52 oS 10-16 V 07-12 04-76 V V V 08-06 05-4, 05 '44 Jan. 27 VI VI 07 51 08-35 04-44 Jan. 3' VI VI VI oS -82 09-46 II 08 Keb. 4 VII 07 -68 Feb. 5 VII 05 -oS 09 55 Feb. S VII VII VII 04-97 06 -S6 04 '^3 Mean Mean by position. 07-24 09-04 05" o7-i6±o" -55 Mean, Mark ea.st of north Diurnal aberration Azimuth of Mark Reduction to ba.se line Reduction to center at Northea.sl Base Angle between Northeast Rase and Stone ^Mountain A/.inuith of Stone Mountain 52 oS 07 -16 -0-31 32 oS 07 '47 -1 -Si -037 So 14 23 65 12 22 2S-94 =0" -55 *The .station i.s i 665 inches, or o"i-0423 to the west and north out of line of the base; the center of aperture wasSmm-? east of Northeast Base. . 36o THE EASTERN OBLIQUE ARC 50. I^AVENDER, GEORGIA. ing power 60. This instrument was used here for the first time.* The azimuth mark was seen under an angle of depression of 0° 37' "3. A set of observations consi.sted of a pointing on tlie mark with telescope direct, followed by 2 observ'ations of the .star, one with image direct, the other with image reflected in mercury. The telescope was then reversed and the star and mark were ob.served as before, but in the reverse order. Observer, F. P. Webber. Probable error of a single result for azimuth ±3" '08 . Siiiiiiiiary of rcsiil/s /or aziimil/i 0/ /lurora, /llahaiiia. a Ursce Minoris nt v.'irious liour :uiKles. a Urs;e Minoris at various hour angles. Date. Position. Mark E. of N. Means. Datt Position, . Mark E. of .N. Means. 1877. June 19 June 20 I I / 66 46 50 '5 49 '4 1S77 June 25 X X c ' " 66 46 467 4S-3 47-5 II II 45 '9 42-8 44 '3 XI XI 49 3 507 50 III III 43-8 1 52 "4 1 48-1 XII XII 53 '4 52 3 52 s IV 54 '5 53 7 XIII 5^-2 57 '3 June 24 IV 52 '9 XIII 564 v V 58-6 59 9 59 3 June 26 XIV XIV 54 9 567 55 -S VI VI 54"4 54 '9 54-6 XV XV 5' -6 527 52 2 VII VII 47 7 48-8 48-2 -XVI .XVI 4Si 4S7 4'i-4 VIII 46-4 .XVII 47-0 VIII 42 '9 44 7 June 27 XVII 5>2 49 I IX IX 47 '5 44 '4 46 '0 Mean 66 46 50-67±o" 72 Mean, Mark east of north Diurnal aberration Azimuth of Mark Angle between Mark and Brandon Azimuth of Brandon 66 46 50 '67 -0-31 246 46 50-98 2=0" -72 349 19 5«"37 236 06 29 35 *The graduation of the horizontal circle was afterwards found to be defective l ;62 THE EASTERN OBLIQUE ARC. 52. KAHATCHEE, ALABAMA. 9 -29 49 '2 — 02 48-9 +0-I 49 "9 -09 50-0 — I 51-6 -2-6 Mean 65 52 49 00±o"'i; Mean, Mark east of north 65 52 49 'oo Diurnal aberration -rO'3i // Azimuth of Mark 245 52 49-3ii;=o-i7 Angle between Mark and Lovers Leap o'txj Azimuth of Lovers Leap 245 52 49 '3i 364 THE EASTERN OBLIQUE ARC. 54. FORT MORGAN, ALABAMA. o\ver, 30 and 40.* A set of observations generally consisted of 6 pointings on the mark, telescope direct, 6 observations of the star, with time and level record. The instrument was then reversed and the preceding observations were repeated, hut in the reverse order. One divi.sion of level ~2"'92. Observer, R. H. Fauntleroy. Probable error of a .single result for azimuth ±i"'i8. Suuimaiy of results for aziviiith at East Pascaffoula, Mississippi. a. Ursa; Minoris near eastern elonKalion, Date. 1847. June 12 13 14 15 iS 24 Position. II III I V IV V Mark W. of N. 147 06 16 '97 17 '55 20 '10 20 78 18-17 18-85 147 06 iS-74±o"'4i a Ursoc Minoris near western elongation. Mark W. of N. A Date. 1S47. Po sition + i'77 June 14 I + 1 -ly 15 III -1-36 iS V — 2 -04 26 IV +0-57 July 9 II — Q-II 12 III 147 06 14-47 19-04 20-15 IS -27 17-90 16-50 +3-25 -1-32 -2-43 -o'55 -o-i8 -f I -22 147 06 i7-72±o"-55 Mean of groups Diurnal aberration Azimuth of Mark 147 06 iS -23 32 53 42 -oSdrO -34 Angle between East Pascagoula and Bayou Casotte 96 22 50 Si Azimuth of Bayou Casotte 296 30 51 -27 I * Two eyepieces used. 1 366 THE EASTERN OBLIQUE ARC. 56. CAT ISLAND 1S55, MISSISSIPPI.

- UJ > cc 2 CO 2 ui •^ O Q 2 _ z or '^ z < ° 5 0- o ^ U UJ ^ £r < ^ H- O 6 o C/5 DETERMINATION OF AN OSCllLATIXi; Si'HIiROII) FOR THF: KECION COViiRED BY THE TRIAXGUEATIOX. A. COMPARISONS OF THE AvSTRONOiMIC AND GEODETIC RESULTS AT STATIONS CONNECTED WITH THIi OBLIQUE ARC. Parts II and III contain tlie necessary stateniuiUs and results for the next (jperation, namely, the direct comparison of the astronomic latitudes, longitudes, and azimutlis with their corresponding values derived geodetically by development of the triangulation upon the Clarke spheroid of iS66. In doing this the geodetic data for the station Hays, Kansas, as given in the account of the transcontinental triangidation and arc of the parallel in latitude 39°, have been adhered to. The\' are: [ (Po= 3'*^ 54 S"'!'"^" \ A,, =: 99 16 16 730 I "'=359 44 19 'cx) Hays lo I^a Crosse. We shall thus .secure .sy.stematic positions which, if desirable, may be made at once available for a determitiation of an osculating spheroid ba.sed upon a surface of witler geographic limits than is contemplated in this di.scussion. As early as the year 1879 the writer made a preliminary compari.son of tlie astro- nomic and geodetic measures then available.* The stations inchuled extend from Calais, Maine, to Atlanta, Georgia. That di.scu.ssion furni.shed the first comprehensive information of the relative magnitude and distribution of the outstanding differences between the astronomic and geodetic results in the United States, the latter as develojKnl on each of two reference spheroids. It led to the adojnion of the Clarke .spheroid of 1866 for u.se by the Coast and (xeodetic Survey. As a matter of general interest, the location oi the ])rincipal ,irc measures and areas oi osculating spheroids is .shown on a Lambert equivalent zenithal projection ujxmi a meridional plane and transferred from a hemi- to a plani-.sjihere,''- constructed by Adolph Lindenkohl, of the Drawing Division, Coast and Geodetic Survey, for this special u.se. Lambert himself pointed out how the whole surface of the sphere could lx.» represented, a fact .stated again in Littrow's admirable work, Chorographie, etc., von J. J. Littrow. Wien, 1833, page 126. *U. ,S. Co.isl ;m(l OtoiUtic .Siirvty K. 371 witli the local deflections of the vertical, the average inagnitiule of wliich, nanielj', 2"'4,* has been deduced from a large number of comjjarisons. It lias, however, been concluded to apply these small and as 3'et rather uncertain corrections in the present investigation. The corrections to all latitude results were computed by Chandler's formulae t except for a few .stations where none were needed and for four stations (Kxupied in 1IS97 and 1898 where Dr. Albrccht's results were introduced in jireference, as contained in his report on the state (jf the latitude \ariation at the close of the year 1899 [Centralbureau der Internationalen ludmessung, Berlin. 1900]. About one-half of the corrections thus computed were found to be belcnv o"' i , a very few reached o""2, and none exceeded o"'25. I"or the whole arc these corrections balance. The effect of the \ariation of the po.sition of the pole upon observed differences of longitude is small enough to be negligible and the .same is true with reference to the observed azimuths, for which the j^robable error of observation always exceeds the small correction due to the polar variation. The headings of the following summar}- of results need no e.xiilanation. The geo- detic latitudes were in all cases referred to the astronomic station unless the two stations happened to be located on the .same parallel or to be identical in position. The relative position of the stations is stated in the preceding abstracts and the reductions there given are applied to the geodetic latitude with the sign reversed. The last colunni con- tains the apparent local deflection of the vertical in the plane of the meridian or the dif- ference (A-G) of the two values in the two preceding cohunns. * Probable error in the direction of the vertical from all parts of India except portions under Hinialay in attraction is about + 2"'8. (Annual Report of the Survey of India, 1803-94.) t Astronomical Journal (Gould's), No. 446. October 14. 1S9S. The formula: are. for the coordinates. ix=ii sin (/-Ti) fl + 0-095 sin (©-308°) \y = 1 1 cos (/ — Ti) 9 +0110 cos (0— 3°) Where Ti = 2 412 646 + 427 o E — o -oS E = e = 0° -.Sij + o -ooo 316 E 1 1 = o" '125 + o'o5 sin (2 414 363 — /) x o°-oi5 Here t and Ti are expressed in Julian dales, / is the epoch of observation, Ti any epoch when the pole of the figure passes the Greenwich meridian between Greenwich and the instantaneous pole of rotation 1 this /<»//<•/ taken as the origin of the coordinates .r and.v), K is the number of periods, t» Uic daily auirular motiiui, / , the radius vector, and J" the sun's longitude at the time /. The variation of latitude /ip = ip ~ '9'' .34 31 37 75 .34 19 '5'«' 34 14 04 ■20 34 oS 47 -45 33 54 21 -82 33 44 59 '3" 33 13 39 'yo 32 22 45-41 31 50 21 -ly 3! 14 47-82 30 41 33 42 30 20 40 -92 30 13 47 -89 2Q S7 25 - 2S o -00 — O -ijA — O -23 — o -03 —0-07 -o. 13 — o -05 -O-OH — Q-IO — o -08 — o'oS — o -10 —0-07 — o -05 —0-04 — o -06 — O 'Ol — 0-02 — Q-O! o -00 O -QO o -00 O -oo — -12 — o -14 — O "20 + 0-17 +0-19 + 0-23 +0-24 + 0-19 + 0-19 +0-07 + 0-02 — 007 +0-25 — o-ii + 0-02 — Q-IO — O'ifi — ot; — 007 + 0-IO — 0-ot — o-oi + 1-) -OS 25 05 39-8H .39-60 57 ■»'' 61 •(>-) 28 -84 55 '05 21 -69 13 42 32 -OS 37 74 1575 04-03 47 '63 21-66 59 iS 39 74 45 '24 21 -00 47 74 33 52 40-91 47 ■•'*8 ?> -5^ 25-68 39 ^-^ 39-22 .57 '51 .55-9' 25 '.I'" 5' 44 12-27 09 S"* 27 -S8 36-64 16 01 02 -93 45 24 19 -05 56-10 35 9' 37 37 iS-si 48-39 2.8-91 33 59 40 -30 -0-63 — o'lo +0-JI -043 H-S-ls •t-3 34 ■r3-6l + 9-42 ■+-3"'4 +4 17 + 1 -pj —0-26 + 1 -lo + 2-39 + 2-61 ~3''3 -2-49 -0-65 +4 '61 + 7-32 ■4-7 ■5'^ -I---,, Revicic of tlic preceding latitudinal deflections. — Takin}>^ in the whole* iuunlx;r of comparisons, there is a preponderance of phis si^ns in the vahies of (A-G), viz: 44 with a + and 27wath a — sign. This inequality is most marked in the southern part of tlie arc where the po-sitive signs predominate, and this is e.si)ecially the ca.se for stations near the Gulf coast. The mean deflection of the last 4 stations is +6" '6, apparently indi- cating a deviation of the plumb line directed toward the Gulf. The average value of 112 {A-G) is +— -- = + i""6. There are .several localities where the latitude stations are crowded together, and, consequently, are .subject to the same regional deviation. For each of these localities it is de.siral)le to substitute a single station of average or repre- sentative value. There are 6 such cases, the latitudes in each group being contained within a space of about i'. For these groups we have adopted the following \-alues: Groups. 20, 21 27. 28 35. 36, 37 3'"^- 39 40, 41, 42 43, 44, 45, 46, 47, 4S These values, when substituted for the respective tabular numbers, make ::fi^A-G) , 106 = H ^= -+- 1 "8 nearh'. " 59 Value .-!-(;. // -3 -JS +3 73 + 1 •11 + 1 •74 — I •2S —0 •26 374 THE EASTERN OBLIQUE ARC. Of these differences 39 are positive and 20 negative. The resulting average ( + 1""8) may be regarded as representing the difference between the standard latitude of the transcontinental arc of the parallel of 39° and that of the eastern oblique arc. This discordance of nearly 2" in the standard latitudes of the arcs at their intersection is not surprising when we examine the regional changes in the values of (A-G) along the arc of the parallel. There are 109 astronomic latitudes connected with the arc of the parallel and 71 with the oblique arc. Of these, 24 are common to both; consequently, 156 independent latitude stations are involved in the discussions of the two arcs. 2. The Astronomic Longitude St.\tions. Coniparihon of astronomic and standard geodetic longitudes. No. Name of longitude station and state. Object of reference. Observed astronomic longitude. Seconds of geo- detic lon- gitude.* A-G. I Calais, Me. Transit ■ 67 16 ,S7'86 53 '92 + 3 '94 2 Bangor, Me. Transit 68 47 02 -60 01 -20 -1-1 -40 3 Cambridge, Mass. Center of dome, Harvard Observatory. 71 07 45-69 44 74 +0-95 4 Cape May, N. J. Transit 74 55 45 'SB 48-03 -2 '35 5 Dover, Del. Transit 75 31 18-45 24 '51 -6-06 6 Washington, D. C. Seaton, transit 76 59 52 '73 60 10 -7-37 7 Washington, D. C. Coast and Geodetic Survey Office, transit 77 00 25 64 3271 -7-07 S Washington, D. C. Old Naval Observatory, small dome 77 03 02-30 06-68 -4 '38 9 Washington, D. C. New Naval Observatory, center clock room 77 03 56-76 62-80 —6-04 Strasburg, Va. Transit 7S 21 3570 39 '54 -3-84 1 Charlottesville, Va. McCormick Obser\-atory, transit 78 31 20-10 21-15 -1-05 2 Statesville, N. C. Transit, near Simenton College 80 53 41 -31 40-44 -Ho -87 3 Atlanta, Ga. Transit, 1S96 84 23 20 07 19-41 -ho -66 4 Montgomery, Ala. Transit 86 17 59 '19 60-92 -173 [5 Lower Peach Tree, Ala. Transit 87 32 40 -94 43 '37 -2-43 [6 Mobile, Ala. Transit 88 02 37-37 33 -83 +3 54 17 New Orleans, I,a, Transit, iSSo and 1S95, Lafayette Square go 04 II '44 12 -16 -0-72 Review of the preceding longitudinal deflections. — Before examining the tabular val- ues {A — G) it is de-sirable to contract the table on account of the regional deflections about Washington by admitting only one in the place of the four closely packed stations. The average value of {A — G) for numbers 6, 7, 8, 9 is — 6"-22. For the.se, number 9 or the New Naval Observatory value —6" '04 has been substituted. The distribution of the 14 stations over the whole arc is fairly uniform. They .show an average deflection Qf c^j[^Q) — _o"-92, the plumb line apparently being attracted to the westward. This amount might be expected from the location of the arc. Thus for one-half of the stations, either on account of proximity to the Atlantic coast or in con.sequence of their location to the ea.st of the principal mountain chains, or for both reasons, negative values of {A—G) might be expected. The.se values are as follows: Cambridge Cape May Dover Washington StrasVjtirg Charlottesville Statesville +0-95 -2-35 -6 -06 — 6-04 -3'S4 - 1 '05 +0-87 Average value = — 2''-50. ♦For reference date see introductory remarks to Part IV. THE DETERMINATION OF THE SI'HI-.kOID. 375 Thu value at New Orleans also has a nej^ative sign, though tlie alxjve reasons do not aj)ply to this location. It has already been remarked in the account of the transcontinental triangulation and arc of the parallel in latitude 39° that Cape May, though directly located on the coast, is distant about 2 13 kilometers (115 nautical miles) from the actual, but submerged, continental border.* At Calais we find the largest, yet moderate, jxjsitive deflection + 3" "94, which probably, in a mea.sure, is due to the attraction of the mass of Xova Scotia lying directly to the ea.stward of the station. Respecting the remaining 6 stations no .special features appear to be present, and the deviations may be indiflferently + or — , the average value being +o"'45. 3. The A.stkonomic A/amith St.vtions. Comparison of as/ronoiiiir and i^iodc/ic arjiiiiii//is of sides of the tiiani^ulalion. Year No. Name of aziimiUi station. State. of observa- tion. Reference .station. Astronomic azimuth of line. Geodetic , ,. azimuth.t ''"^• I Cooper Me. 1859 Howard 35 > 53 1 2 05 09-93 -i-2-l2 2 Howard Me. 1859 Pigeon 63 54 45" 42-96 4-2-15 3 Humpback Me. 1858 Cooper 254 42 32-36 27-80 -1-4-56 4 Mount De.sert Me. 1856 Ragged Mountain 78 30 46-57 45-89 -i-o-68 5 Mount Harris Me. 1S55 Humpback 254 35 10-62 06 04 +4-58 6 Ragged Mountain Me. 1854 Mount Pleasant Si 48 45-00 41-73 +3-27 7 Cape Small Me. 1851 Sabattus '53 18 63 •51 59-9 +3-6 8 Sabattus Me. 1853 Mount Independence 24 31 23-5' 20-64 -1-2-87 9 Mount Independence Me. 1S49 Agamenticus 26 55 48-60 48-58 4-0 -22 10 Mount Plea.sant Me. 185 1 Mount Blue 205 59 21-56 '7-53 4-4-03 II Agamenticus Me. 1.S47 Thompson 2 5fi 55 '51 55-92 -0-41 12 Gunstock N. H. 1S60 Mount Pleasant 217 43 33-60 27-36 -1-6-24 13 Unkonoonuc N. H. 184S Onnstock 196 .35 20-38 16 -68 + 3-70 14 Thompson Mass. 1S46 Manomet 35> 21 41-86 40-40 -I-I-46 1.5 Wachusett Mass. i860 Bald Hill 24 17 41-45 32-42 -9 03 16 Har\'ard Observatory (dome) Ma.ss. 1869 Blue Hill 356 25 264 25 1 + '-J 17 Blue Hill Mass. iS4,S Manomet 305 57 30-05 29 89 ■fo-i6 18 Shootflying Mass. 1S45 Manomet M3 03 22-74 ■9 5 +3-2 19 Indian Mass. 1845 Copecut 135 35 58-82 62-6 -3-8 20 Copecut Mass. 1S44 Blue Hill "75 17 06-5 04-04 -1-2-5 21 Beaconpole R.I. 1S44 Blue Hill 22S 55 17-24 '7-53 -0-29 22 Spencer R.I. 1S44 Beaconpole 185 57 33-02 36-5 -3-5 23 Mount Tom Mass. 1S62 Monadnock 212 37 21-74 '5 -'3 4-6-61 24 Sandford Conn. 1S62 Ruland 5 50 25-28 15 -86 4-9-42 25 West Hills N. Y. 1865 Woostcr 174 57 3S-32 33 87 4-4-45 26 Beacon Hill N.J. 1875 Weasel 183 35 29 89 29 32 4-0-57 27 Mount Rose N.J. 1852 Mount Holly 7 46 55-59 58-26 -2 67 28 Yard Pa. •854 Lippiucott 547 17 38 -57 37-09 4-1 -48 29 Priucipio Md. 1866 Turkey 1 34 43-5' 34 59 4- 8 -92 30 Cape Henlopen Light-House Del. 1S97 Brandy wine Light- 1 louse '73 45 ■7-33 15-29 4-2-04 3' Marriott Md. iSjg Hill 96 37 43-36 35-04 4- S-32 32 Webb Md. 1 S,SO Soper SS 59 49 '24 42-70 4- 654 33 Hill Md. 1S50 Webb 319 46 5789 51 -13 4- 6-76 34 Soper Md. 1 ^.so Webb a6S 49 23 -46 IS -14 + 5-3» 3.S Seaton DC. l.Soy Hill 265 32 53-76 42-33 4- II -45 36 Causten n. C. l,-;?! Soper 2IO 54 41-78 58-3 4- 3-5 37 Sugar Loaf Md. 1879 Bull Run 32 29 16-79 22 -jS - 5-49 3S Maryland Heights Md. 1870 Bull Run 35S 43 06 -SS 'O-54 - 5-«6 * Page S37 of Special Publication No. 4. " The Transcontinental Triangulation.' t For reference data see introductory remarks to Part IV. 376 THE EASTERN OBLIQUE ARC. Comparison of asfronoinic and geodetic aziiiiuths of sides of the triangulation Name of azimuth station. 39 Bull Run 40 Clark 41 Long Mountain 42 Elliott Knob 43 Moore 44 Young- 45 King 46 Paris 47 Currahee 43 Sawnee 49 Atlanta Middle Base 50 Lavender 51 Aurora 52 Kahatchee 53 Ethridge 54 Fort Morgan 55 East Pascagoula 56 Cat Island 1S55 Year State. of observa- Reference tion. Va. i,S7i Peach Grove Va. 1871 Bull Run Va. 1S75 Spear Va. 1S78 Humpback N.C. 1S76 Buffalo N.C. 1S76 Poore N.C. i«77 Benu S. C, i'"*75 Wofford Ga. 1S74 Rabun Ga. '873 Currahee Ga. 1873 Stone Mountain Ga. 1S74 Kenesaw Ala. 1S77 Brandon Ala. 189S Horn Ala. 189S Lovers Leap Ala, 1847 Cedar Point Miss. 1847 Bayou Casotte Miss. 1S55 Mississippi City IgU 'att ();/~continiieii Astronomic azimuth of line. Geodetic a-/dmuth. A-G. 263 53 2S-15 30-60 - 2-45 202 19 2777 28-81 - 1-04 223 2S 4174 46 -62 - 4-88 303 25 24 '37 22-28 + 2-09 158 33 3''I9 32-10 — 0-91 126 52 33 '69 52-65 + I -04 141 33 36-9 39 '3 - 2-4 267 18 I5'I7 15-89 — 0-72 tSS 10 27-89 26-00 + I -89 245 34 26-12 28-93 - 2-81 312 22 28-94 32-71 - 3 77 300 1 1 59'il 61 -oS - 1-97 236 06 29 '35 31 '43 - 2-oS 253 32 1 2 -80 15 '48 - 2-68 245 52 49 '31 52-05 - 2-74 143 59 45 '61 50-69 - 5-08 296 30 51 '27 53-20 - 1-93 192 II 14-3 08 -4 +5-9(?) Revieii' of the preceding aziviuthal deflections. — We recognize as their main feature systematic but small po.sitive deflections, i. e., plumb line attracted westward for that part of the arc which lies north of the thirty-ninth parallel, and small negative deflec- tions for the part .south of that parallel, thus showing for the whole arc a small predomi- 86-7 nating plus value or + i"-55. Omitting the last azimuth, No. n 56 56, as doubtful,* and using No. 33 in.stead of the six closely clustered values in the vicinity of Washington, i. e. , Nos. 31, 32, t,},, 34, 35, 36, the average value for the oljlique arc becomes ^ = -|- =+o"-9i. This represents the discrepancy between the average azimuths of the arc of the parallel in latitude 39° and of the oblique arc, and, considering its small size, the general azimuthal directions of the two arcs may be taken as being in satisfactor\- accord. A remarkable feature in the tabular values of (A-G), and one that had been known for a long time, is the large regional deflection existing in that part of the triangulation common to the two arcs. The average deflec- tion observed at the six .stations — Marriott, Webb, Hill, Soper, Seaton, and Causten — is + 7"'o, the plumb line being attracted to the westward. If we convert this value into a corresponding longitudinal quantity, we have JA= — z/«/sin <^= — ii""i, which agrees in sign but exceeds in amount the mean value {A-G) = —6"'2, as found from the four longitudinal deflections in this region obtained at stations, only one of which is identical with any of those named above. Considering that the present adopted azimuth depends upon 73 azimuth determina- tions or stations of the triangulation along the 39th parallel, any new or independent correction that might Ije deduced for standard value in the oblique arc would probably not differ from it h\ as much as one .second. *The last value of our table is marked as doubtful for the reason that the accuracy both of the astronomic and geodetic measures is inferior to that of the other tabular re.sults; and. moreover, its appearance with a large positive value (pointing to westerly deflection) in a region where minus values predominate imparts to it an anomalous char- .acter, especially in a flat region of quaternary formation without any surface indications to justify or account for a reversal in the direction of the disturbed noiiual of the place. No further use will be made of this station iii coiinec- lion with azimuths ' — v^ ,/ » THE DETERMINATION OK THE SI'HHROIO. 377 B. DETERMINATION OF A SPHICROII) MOST NEARLY RIv PRI-SKXTIXO THAT PART OF THE EARTH'S SURFACE LYINO BETWi:i:x MAIXl- AND LOUISIANA AND ALONG THE REGION COYERED HY THE TRIANGULATION. The )ii(tliod and fonuitltr employed. After having assumed a reference sj)heroicl representing the figure of the eartli as closely as may be, and placed in position thereon, and having developed the triangula- tion upon its surface, the problem next to be solved is t(j determine corrections to the dimensions of the reference spheroid whicli shall make the sum (jf the squares of tlie apparent discrepancies between geodetic and astronomic results a minimum. In other words, we are to determine a representative or ()sculator\- spheroid wliich shall most nearly harmonize these measures, necessarily lea\ing outstanding the mere local deflec- tions of the vertical at the stations involved. For this purpo.se it has been thought most expedient to follow the theoretical development as presented by Capt. A. R. Clarke, R. E., in the Aeeounl of the Principal Triangulatiou of Great Britain and Ireland/- In this work the method is developed and applied to the computation of a spheroid who.se (Hmensions were in l)est accord with the curvature of the surface of tliese countries. Let P beany point on the actual irregular or disturbed surface (2) and /'_ its projection upon the surface of a regular or reference spheroid ( i ) ; through /' on the surface (2) let a sy.stem of rectangular axes of coordinates <*;', /;, T, lie drawn, so that B, is directed to the north, //to the east, and C^ to the zenith. For an\- two points A and B connected b>- triangulatiou let f/^ if' l)e their observed or apparent latitudes, JA their observed or apparent difference of longitude; also, let the direction of the meridian be observed at each place. If A,, B, are the projections of A and B and .s- their distance, and OL the observed azimuth of B at A, and a' the reverse a/.inuuli, or that of A at B. and if ^,, ^/, «,, ^v/, and A\^ refer to the points A,, B,, then ' """"-^ '*" ) " ■ (sec (p' sui <«,')30 , . , , /sin

' sm <»' )d6 *Orilii;uiCf Survey, l.oiuloti, is^S. pp. 6ck) ;uu1 folUnviiii;. .Sec ;i1mi Chapli-r \U of Cl;>rke'< G«rcKlesy; (Oxford. iSCSa tcr, Hclmert, Uoherc OcoiUUic, Vol. i, pp. ,s,vS-5,;'v I.fip/ig, iSSo, 378 THE EASTERN OBLIQUE ARC. where These equations may be written in the form: The values of the absolute terms are: ,ti = ( calculated -observed) latitude ;f,= (observed — calculated) longitudexcos q>' ;^,= (calculated— observed) aziiuuthXcot -- Putting hence (i—c^ sin^ ^)''^ looil = /, and ^- '""^ cos^ 'U{(p+5(p')=n' _ [i-g° sin'^ V,((pM-/2 M {i-ey also writing /^(arc icjo") for/ and t'(arc 100'^) for f, then Qe=/.i'{q>'—' sin A\ bi=?>\\\

ct)S •}>' cos J\ i-sin ii> sin «>' and sin a -cvvs ip sin J,\ sin • tThe new ol)seivatory was connected by local trianKiilation with the Coast and Oeoiletic Sur\-ey trianindalion by Prof. W. Harkne.ss, .\.strononiical Director in iSo,; and :Sai, and by .Assistant K. l>. Preston in is»i4. The work of .\.v»-»tant C. Jnnken in iSSi is involved in the adjustment of the v;oodetic connection. 38o THE EASTERN OBLIQUE ARC. Collection of certain constants and tabular quantities required in the computation for establishing the conditional equations. For Clarke's spheroid of 1866 we have log a = 6 '804 698 57 log b = 6 '803 223 78 log ^==7 -830 502 57 with the following data for the reference station,

^ 6-687 692 I 35"= J(^)° = iS-3 674 353^ 655 36 637 36>^ 619 37 600 37 K 582 38 564 ■38^ 546 39 527 39'-^ '^{'A 6-687 509 490 471 453 434 415 396 377 359 340 ° = i8-8 (P 40° 4-O^A 41 4i>^ 42 42K 43 43 K 44 44 M 45 6-687 321 302 283 264 245 226 207 188 169 150 131 TH]-; I)]-,TKRMINATION OF THK SI'HF.kOII). 3«I Values of lo,i( ii' sin i" lichvi'fu latitudes ^i>^ atid ./^l^ qj' 3o°oo' 6 '544 (K) lo 42 Si 20 41 61 30 •540 41 40 39 2(1 50 37 99 31 •536 77 10 35 54 20 34 31 30 ■533 07 40 3 J S3 50 30 5'^^ 32 •529 33 10 2S 07 20 26 80 30 •525 52 40 24 24 50 22 95 33 •521 66 10 20 36 20 1 9 06 30 •517 75 40 ■6 43 50 15 'I 34 •513 7^ 10 12 44 20 I I \o 30 •509 75 40 08 41) 50 07 04 35 6 -505 67 du/ 9 54 07 74 6-405 93 158 ■58 '59 '59 160 161 161 162 '63 164 164 ■65 166 167 167 1 6.8 169 169 170 '7' 172 '73 '73 '74 '75 176 176 "77 178 1 78 '79 180 181 Selectioi/ of stations for 7oliich the results of eoiiif>arisoii of astrououiie and f^eodftic dalu uere admitted into the equations of eondition. In a preceding table there has been exhibitetl a comparison of the astronomic and geodetic latitudes for 71 stations. If all of these were inclnded in the discnssion. the labor of computation would be uiniecessarily great, since practically the s;ime accuracy of the results can be attained by a judicious selection of a much smaller numlier of lati- tude stations, provided they are uniforndy tlistributed over the whole region of the arc. 382 THE EASTERN OBLIQUE ARC. The following table contains these selected stations with their geodetic positions (to the nearest half second), together with the computed distances ^ and azimuths a' to the reference station at Washington, D. C. For these stations the value, "S (A — G) n = + 2"' I, is nearlj' the same as that previously derived from all the stations after the mean value for each of the 6 groups had been introduced in place of the separate values. No. Name of latitude station. Geodetic lati- tude 2r -■ I 27 18 I 26 40 51 42 23 9 Statesville 35 46 54 80 53 40 + 3 49 37 4 22 '4 43 CJ4 37 10 Atlanta 33 44 56 ^4 23 19 '5 -U 7 '9 16-5 7 5' J 20 4^^ 45 03 II Montgomery 32 22 37 86 18 01 + 9 '3 58 9 56 43 4^ 24 38 12 Lower Peach Tree 31 50 18 5 87 32 43 + 10 28 40 II 04 59 47 31 10 13 Mobile 3" 41 29 88 02 34 + 10 5.H 31 12 1 1 09 44 41 45 14 New Orleans 1H95) 29 56 51 5 90 04 12 + 13 (X> 09 13 57 22 46 39 S"^' The data for the computation of the distances of the several astnniomic a:iiiiut/i stations from the initial station and of the azimuths of the latter from the various stations will be found in the following table, together with the re.sulting values of H and o-'. As was the ca.se with the latitudes, we have here a .surplus of .stations at which astro- nomic azimuths were mea.sured. Much lalxir ma\- therefore be saved without incur- ring au}' sensible loss of accuracy in the results b\- the selection of a more limited number of stations uniformly distributed, as nearh- as may be, over the whole arc and properly representing the deflection over every part of it. For these 34 positions the average value of (A-G) is i'"9, the same value found from all the stations. * United States Naval Observatory. Georgetown Heights. Washington, D. C. t McConnick Observatory. 384 THE EAvSTERN OBLIQUE ARC. No. Name of azimuth station. Geodetic lati- tude sirT £ ,= -5 "Sr (-() •9.S54S o i(j6S// |()i6,si// •3'7759^' c j= 0-96 +0 ■9X60 ni(i.).S 9 ''Ssos • 3 "6825 63=-! I -83 ( o. 9.S7.S no97S 9 73.5" • 3 •6fj.S2 £4 = 4 I '43 [-0-9927 "■"7.5'^ 9-67«) t-3 M'^^-^ ^5 = -J"33 I 0.9881 t)-()965 •S-.H.S95 +3 '.3677 ^6= -i'59 fo-9941 0-0683 •'-!-6i43 +3 ''4X3 £ 7= 2 76 f o -993 1 o ■< .738 8 0935 4-3 -0268 ?^= 2-17 1-0 -ggj'"^ 0-0697 7-1973 +2-7441 £ c^= I -49 -| o -9954 -o -o6cx ) 6 -864 1 + 2 -5997 £.o=-hi-7o +0-9939 —0-0693 6-1328 +2-4135 £,, = +o-22 +0-9970 — 0-04.S4 5-6324 -2-1731 ^12=41-30 +0-9936 —0-0709 49244 20272 1.3= 1-0 '56 (0-9974 -0-04,51 4 -.1093 • 1 -7109 ?i4=+3'36 -1-0-9980 -0-0399 -3 '2074 •1-3042 ?.5=-3-47 -f 0-9988 -0-0311 -2-4765 10117 S,6= 6-72 +0-9996 0-01,84 — '-'^'79 0-7376 1,7 = + 1 -80 +0-9998 o-oii6 — 1-1667 +0-4758 £,8= -4 -oo +0-9999 o 0088 — 0-6352 •0-2619 £,p=|-I-I5 , +1-0000 n -OtXTO 0-0000 I ()-(XXX) S2o = -|-o-io +0-9994 0-0217 ; ()-279o i)-()978 ?si=— 0-38 (-0-9999 I 0-0103 + I 0730 0-4466 S2==+o-43 +0-9992 +0-0246 + 1-35,56 0-5496 £2, = — 3-34 +0-9994 +0-0221 + 28818 — 1 ■;28| ?24 = ^3'6i +0-9984 +0-0353 +4-4X82 1-9447 £j5=— 9-42 +0-9980 10-0392 -f- 5-6629 -2-5008 £26=— 3 '84 +0-9973 ! 0-0465 (6-6332 2-9595 £„j=-~i-io +0-9939 (0-0690 . 7 ■96.54 -3 "5375 £28 = — ! -lo +0-9923 +0-0776 -r .S-5469 -3 7925 £25=— 3-18 +0-9918 -(o-o8oi J 9-4168 4 -242S £^o=— 3-83 +0-9869 +0-1014 -' 10-5494 -4-6986 £3, = — 7 -87 +0 -9870 +0 - looS -^12 -024 1 5 -5387 £3^ = — 2 -49 +0 -9S33 ' o ■ 1 1 43 t 1 3 - 1 250 6 -0530 £33 = +o-65 +0-9816 ;(i-i2ii2 -t-14-2331 —6-6521 £34 = — 4-61 +0-9817 101196 :I5-I9i8 —7-2431 £35= -7 '58 +0-9818 1-0-1194 -15-9952 —77455 £,,,= -7-31 +o-9743£ +0-1414?/ .-16-7861/^ — 7-9Si9r' 4192 — No. 7 — 02 — - — 25 386 THE EASTERN OBLIQUE ARC. Conditional equations derived from longitude comparisons. 77, =+2 78 +0 -1206? +0 -98737 — 13-3036// — 2 -6324- ?/2=+o-99 +0-I0I5 +0 -9899 — u -2689 — 2 -2298 V 3 = +070 +0 '0697 +0 -9958 - S-0733 -I -5975 '/4=-i '83 +0 -0234 +0 -9998 — 2 -902 1 -0 -5743 '/.-, =— 470 +0 '0170 +0 -9998 ~ 2 -0968 —0-4146 '/ c=-4 70 "OOOO + I -OOOO -OOOO o-oooo '/7="2-9S — "0142 +0 -9999 -1- I 7565 +0 -3476 77 ^=-0-83 -0-OI57 +0 •999''5 + I -9786 +0-3915 V<)=+o7i ^0 -0390 +0 -9978 + 5 '2098 + 1 -0309 '7i.,= ^o-55 —0 '0708 +0 -9932 + 9 '9653 + 1 -9719 'Ai = — I '46 —0 -0859 +0 -9893 + 12-5722 + 2 -4877 Vi, = -2-o6 -0 -0959 +0 -9870 4-14-2656 +2 -S228 7i3=+3"04 — '0972 + 0-9841 + 14 -9586 H-2 -9599 7u=~o-62 -0-1123= +0 -9801// ^17 -7166// ^3 -S^SS: Conditional equations derived from azimuth coniparisons. 7i5=- 2 -12 +0 •2359£ +0 -8762// — [3 -0504// -2.5823; 'A6=- 4 -58 +0 -2207 +0 -8797 - 12-1795 — 2 -4100 717=- -70 +0-2198 +0 -8S80 - r2 -0170 —2 -3778 '?i8 = - 4-63 +0-1960 +0 -8852 - ro-7734 — 2 -1318 '7i9=- 2 -96 4-0-1747 +0 -8954 - 9 '5081 -I -8814 ?720= + 0-44 +0 -1621 +0-9117 " 8 -6702 — I -7156 7M=- 6-57 +0 -1442 +0 -9079 - 7 7540 -I -5343 ?^2= - 3 '97 +0-1400 +0-9173 - 7 -4540 -1-4750 '7=3 = - o-i8 +0-1544 +0 -9300 - 8 -0914 — I -6011 '7=4=- 7-28 +0 -1 146 +0-9318 — 6-0119 -I -1S96 7=5=-- 10 -66 +0 -1084 +0 -9464 - 5 -5994 — I -1080 1h6= — 5-15 +0 -0972 +0 -9593 - 4 -9506 —0 -9796 '727=+- 3-14 +0-0631 +0 -9692 - 3-1873 —0 '6307 '7=8= — 177 4-0 -0456 +0 -9775 " 2 -2853 -0 -4522 7729=- 10-78 +0-0291 +0 -9856 - I -4459 —0 -2861 '730 = " 2-54 +0 -0552 + 1 -0025 - 2 -6928 -0-5329 7731=- 8-38 +0 -0052 + 1 -0005 - -2538 —0 -0502 '732= + 4-47 —0-0179 +0 -9910 + -8830 +0-1747 '733 = + 3 '04 — -0177 + 1 -0008 + -8638 +0-1709 '734 = + 1-32 —0 -0264 + 1 -0133 + I -2729 +0-2519 %5= + 6 -41 —0 -0582 + 1 '0363 + 2 -7478 +0 -5437 »736=~ 2-66 —0 -0634 + 1 -0159 + 3 '0528 +0 -604 1 '737= + I -23 —0 -0945 + 1-0571 + 4 -3768 +0 -8660 %8=- I -44 —0-1069 + 1 -0735 + 4-8751 +0 -9646 '739= + 3 '40 —0 -1284 + 1 -0S67 + 5 -7809 + 1-1439 '740= + 1-03 —0-1626 + 1 -0922 + 7 -2736 + 1 -4393 '741=- 275 -0-1939 + I-IOI7 + 8 -5856 -f-i -6989 THE DETERMINATION OK THE SPHEROID. 387 C 'o)ulUional cqitalions derived from a-jiinn/h (oiii/xirisoiis -ctjiiliiiuefl. // '742=+5'6i — o •2250 ^1-1173 1 9-.Si3() -1-9417 743 = + 2-89 —0-2536 I I -1028 .11-1790 •2-2l2(J V^i = -\' 3 '"7 —0-2823 i ' lo.S' -112-3928 4-2-4522 ^5 = + 4'09 -0-2947 I 1 1315 -112-6422 4-2-5016 746=+ 4 '37 -0-3266 + 1 -1650 H 13 6023 -t- 2 -6916 '747 = + 8-72 -0-3775 f-1'2252 4 14 •9407 +2-9564 '748=+3'3o —0-3939? +1-21S7V ^15-6464^ -f3-096iz' /•'oniia/ioii of iionnal equations. The types of a latitude observation equation and of a lonj^itude and azimuth equa- tion are: i,^=ni-\-ak^br]^cu-\-ev then ^ + 13-8089 25 -06432 + o '2032 + 22 -6054 - 9 -7844 + 2571 -4804 —1 121 -6132 + 494-2387 o=-r- 0-4477 o=- 10-4552 o=~ 49-5751 o=— 9-8110 From the azimuth ob.servations: 10 -2707//- 40-1059 414-6253 - o=— 17-9120 o=— 13 -1179 0= +833 -7203 0=+ 164 -9719 hence by combination: I •1515^- I -4576'/- 52 -7266«- + 35-1172 + 41 -5066 ^ + 2453 -3579 - 2 -0324?' 7 -9363 279-9192 55 -3890 10-43312' + 8-2132 + 485 -4576 + 96 -0600 1. 10=- 91 -9175 Q= — 27 -6522 0=^257 -6426 .0=4-408-5423 The solution gives — -^36 -71 19=- I -5573'/- 27-2996//- 37-52982' +49-1293 + 104-2179 + 6-3651 +6439-4636 - 356-2364 + 645-6877 |= + i -895 898 with residuals 0-0000 ?; = +0-862 056 0-0000 « = — 0-077 671 6 0-0002 lz;=— 0-573 878 0-0002 TIIK I)KTI-:kMI\.\TI()X OI' TIII". SI'UHkOID. 3«^9 whence we i^vt yif ~2^o' 2 and tin- eciuatorial radius hecomcs 6 ^yJS 2i'/)-4 — 240'3 6 377 966'2 meters; we have also i^-7' (arc lor/' ) - — ovxjo 27S 22, hence the new r - o"oo6 768 7 — o'ooo 278 2 — o'oor) 490 5 (lb .1 Let * -^ ir and or the conii)ression . then : =fii ^ Ui^-i Ui' ^ <«!■• :o'n()3 250 5 hence the compression — the resuitinti vahie of /' is 6 377 966'2 — 20 7; 307 -r/ 6 357 228'5 meters. Snbstitutinji; tin- \;dues lound for '35 26 Kiutj 9 ITnkoncioiuic — 61 27 Currahee in Thonipsou + 2-63 2S Sawnee II Mount Tom + 1-27 29 .\llama 12 Manoniet + 2-35 3" Kalialchee 13 Sandfonl + 1 76 3' Montijoniery 14 West Hills + 4 74 32 Lower IV;. ch Tree 15 Beacon Hill - 1 99 v>3 Coon 16 Yanl -5-'2 34 Mobile 17 Principio 43-51 35 I'orl Morjjau 18 Pooles Island — 2 -21 36 New ()rle:ins -t-3 05 -f2-o6 -rl 70 -t-2-55 -094 —0-92 -6-52 -" 73 -2-26 -^2 36 -fo-47 -l-ooi -3 67 + ' 93 +5 '33 ■1-0 '33 -2-41 — 2 "07 390 THE EASTERN OBIJOUE ARC. Resulting values of ^ and ?/ a I the ohscrviiig stations — continued, station. ij No. Station. I* Calais 2 Bangor 3 Cambridge 4 Cape May 5 Dover 6 Wa.shington 7 Stra.sbiirg 8 Charlottesville 9 Statesville lO Atlanta II Montgomery 12 Lower Peach Tree 13 Mobile 14 New Orleans i5t Cooper i6 Humpback I? Mount De.sert iS Mount Harris 19 Sabattus 20 Agamenticus 21 Gunstock 22 Unkonoonuc 23 Blue Hill 24 Mount Tom +6-41 25 Sandford -8-55 +4 '19 26 West Hills —3-20 +3 -24 27 Mount Ro.se +471 -0 -38 28 Yard — 0-46 -3 '41 29 Principio —9 '60 -3 -84 30 Cape Henlopen Light-House — I -07 -2-49 31 Hill -7-46 -0 -37 32 Maryland Heights +5-13 -I-0-5I 33 Bull Run + 371 +0 '37 34 Clark + 1 '90 -3 "17 35 Long Mountain +6-68 ~4-I2 36 Elliott Knob — 2-48 +0 -85 37 Moore -fl -12 -3 '37 38 Young -1-65 + 1-58 39 King + 3-00 - 1 -07 40 Paris +0-27 + 279 41 Currahee -3-81 -I -44 42 Atlanta :Middle Base +4-28 ~o '04 43 Lavender + 1 "23 -^3■2o 44 Aurora + I-I2 -4-04 45 Kahatchee + 2 -08 -I -48 46 Ethridge +2-15 +2-46 47 Fort Morgan +6 -20 -5-10 48 East Pascagoula +0-6I We have '^BB and .^'/v before and after chang-e of spheroid. Old spheroid. New spheroid. From latitude equations From longitude equations From azimuth equations 506-5 265 -9 83-1 14' '5 789 -2 519-8 From all equations I 378-8 927 -2 The precision of the adjusted or resulting value of the length of the equatorial radius and of the compression as found from the measure of the arc. To find tlie prol^able errors of the elements of the resulting spheroid we have to determine the mean error of a single observation or that of the unit of -weight, as well as the weights of the values of ii and v as obtained from the solution of the normal equations, whence the probable error of the result for the equatorial radius a, and for the compression or -, readilv follows. Stibstituting the values of B, ?/, /i- and :- resulting from the solution of the normal equations in the equations of condition, the re.siduals represent the respective deflec- tions at the stations. vSquaring and siunming up the.se re.siduals, we get ;«^ = ii— --• *,Values I to 14 from longitude equations. t Values 15 to 48 from azinnith equations. THE DETERMINATION' OF THE Sl'HHkOID. 39i where ;;/ = ineaii error (jf the unit of weij^ht, n tlie mniiherof observations or stations, and ;/ the munl)er of normal ecjuationsor unkncnvns. Tlie weiglit of any one of the unknowns is found in the tisual way by means of tlie sohition of the modified normal or weight equations; thus, for the third unknown ii and for the ])recedinj,'' iiyj)othesis of equal weijj^ht to the ol)ser\'ations we have; "= t 3fi V'ly '/. 1 'S.Sy.S '/-• 27 '2996 qn- }>! -529^ 7i 0= 49129.^ • 104-2179 r 6-3651 ■ = 16 439 ■46;,6 -356 -2364 "= ' 64s -6877 Here ])othesis (i ), which assigns etjual weight ' r«'= i) to the olxservation equations, we get ;;/= / — = ±3"'4o; the weight equations in connection with n and i< give: and (y,= f O -CXX322I3 173 = — o -0003659 (7„=-l o -iXX)i6S2 (7, = +o -0001092 q^ = -*'0 -0018212 y5=-o -0003946 ^6=4-0 0001092 ^v = -^ o -( « 1 7 1 S,S hence ??i^,= ±o'044i, and the corresponding value ;«,= i36"4, and the probable error of " ■' - .'-^ -■ -i^v^io , ,■! 1 .,,i,.,,tt the weight J as most smtaDie. X„ the .iscnssion of the or.inance snrve. of ..real Hrita.n atul IrtlanO Car.e a.iopts the .e . THE DETERMINATION OF THE SPHEROIU. 393 I -5 '34 I + 5 •19 15 " 39 2 -0-65 2 ^3 •16 16 -219 3 -F2-i8 3 + 2 ■50 '7 + 1 -68 4 -M-87 4 — •64 18 2-42 5 -0-89 5 3 •61 •9 '91 6 — I -02 6 3 ■85 20 2 40 7 -2-15 7 2 •31 21 4 76 8 -1-45 8 •21 22 -2-lS 9 -070 9 -f-o ■96 23 • 1 71 10 + 2-55 10 f-o •23 24 5 -66 II + 1 -19 II ~2 •07 25 911 12 4-2-30 12 i 2 •87 26 -3 -65 13 + 171 13 + 2 •16 27 • 4-39 14 + 4-68 14 — I •81 28 -0 63 15 -2-03 29 -976 16 -5 -16 30 -'•33 17 -r5 '48 31 -7 -52 18 —2 -24 32 -5 19 19 + 3 '02 33 ^3 77 20 +1-98 34 + 1 -98 21 +1 -69 35 +6-90 22 + 2-53 36 -2 24 23 —0 -96 37 -f I "SO 24 -0-94 38 -I 24 25 -6-52 39 + 3 '47 26 -075 40 +090 27 + 2-23 41 -308 28 + 2-34 42 4-5 '2 29 + 0-44 43 + 2 -22 30 0-03 44 + 2 -21 31 -372 45 + 3-19 32 + 1-87 46 + 3-34 33 +5 -25 47 + 7 '52 34 + 0-24 48 + 1-99 35 ~2 -52 36 -2-17 trom The prol^able error of a sin_e;le latitude is o'674 J ~ = ±i""94 as computed fi ^ 36 — 4 the ^6 latitude discrepancies and tliat of a sin,t;le latitutle or loiiijitude ob'TA-.''^ "* "'* = > 5^ — 4 ±i"'90 as computed from the ^^ latitude and the 14 loni^ituile discrepancies. 4192 — No. 7 — 02 26 Comparison with Other Spheroids. The following table is presented for convenience of reference or comparison of the resnlting spheroid with a few other spheroids (of revolution): Equatorial Polar semi- ,-„.„„,<.<.e,. Spheroid of — radius i; diameter b a — h. in meters. in meters. (a-b) a. Ressel, 1841. From 10 arcs of the meridian, total 6 377 397 6 356 079 21 318 1/29915 amplitude 50° 34'. ~-^ "' Clarke, 1858.* Special spheroid for surface of Great 6 37S 494 6 355 746 22 74S 1/280-4 -f-QO ~^~S '\ Britain and Ireland. Range in latitude 12°, the ^ ^ same in longitude; 75 astronomic stations. Clarke, 1S66. I'rom five meridional arcs, total 6 37S 206 6 356 5S4 21 622 1/295 'o amplitude 76° 35'. Clarke, 1S80.* From five meridional arcs and Ion- 6 37S 249 6 356 515 2\ 734 1/293-5 gitudinal measures, total amplitude 88° 59' -8 equatorial degrees. U. vS. Coast and Geodetic vSurve}-, 1900. Eastern 6 37S 157 6 357 210 20 947 1/304 "5 Oblique Arc of the United vStates. Total ampli- — ^^ ~'^ tude 23° 31'; 84 astronomic stations. Harkness, 1891. From "The Solar Parallax and 6 377 972 6 356 727 2! 245 1/300-2 Related Constants," Washington, 1891, p. 138. ~ ^ " * For conversion of English feet into meters Clarke's determination of 1S66 wa.s used, viz: r ft. =0-30479727 m, I m. =3-28086933 ft. 394 1 ■ifffiiffr S^m^f^S^yfyS^ifCf^^^ ^f^'^M %S5?«5«?S^S«5?%%55«?^.,x/,SS5*««%«%^!«5^^